please I need help with these questions, this is my 4th time posting it!!!

it is a 4 questions

1- What is the most important feature that distinguishes takaful from conventional insurance? (5 marks).* Your answer 2- Explain briefly the difference between a pure wakalh model and a pure mudarabah model in Islamic insurance. (5 marks).* Your answer 3- How the author consider the relationship between policyholders and TOs as a principal-agent model. (5 marks) * Your answer 4- What are the main conclusions of this paper? (5 marks) * Your answer Journal of cosmic Behavio Organization 105 (2015: 135-144 Contents lists available at ScienceDirect Journal of Economic Behavior & Organization ELSEVIER journal homepage: www.elsevier.com/locateljebo Crows Mark Optimal incentives for takaful (Islamic insurance) operators Hayat Khan Department of Finance. Le Trobe Business School, Faculty of Business. Economics and Law, La Trobe University, Budaoru, Melbourne VIC 2016. Australia ARTICLE INFO ABSTRACT Article history Received October 2014 Accepted 2 November 2014 Available online 11 November 2014 oficerion 14 DS 13 Keywords: Takaful Islamic insurance Optimal incentives Wakalah Mudara Agency theory The relationship between policyholders and an Islamic insurance (takaful operatoris in essence a principal-agent relationship. This paper analyzes the power of incentives offered to takaful operators in mitigating problems associated with such a relationship. These incen- tives include wakalah, an upfront agency fee as a percentage of premiums, muderabah, a share in investment income from technical reserves and surplus-sharing a share in the insurance surplus). The paper concludes that all incentives offered to takaful operators must include surplus-sharing and that offering mudarabah in the presence of surplus-sharing is optimal only when the risk-adjusted return on investing technical reserves outweighs a similar retum on effort exerted in underwriting risks. A wakalah hybrid is also recom- mended as it induces the operator to increase the size of the pool that, in turn, reduces average risk to the benefit of policyholders. 2014 Elsevier BV All rights reserved, 1. Introduction Islamic insurance (takaful) is a relatively new but growing segment of the Islamic finance industry. As far as incentives are concerned, the most important feature that distinguishes takaful from conventional insurance relates to the nature of the contract that governs the relationship between the policyholders and an insurance company. Conventional insurance is primarily a contract of risk transfer as it transfers the risk of loss insured from the policyholders to an insurance company against an agreed amount of premium The insurance company owns the premiums written and any surplus or deficit generated by the insurance operation Policyholders only have the right to claim under conditions identified in the insurance policy. Islamic insurance on the other hand is a contract of risk sharing among policyholders. The insurance company referred to as the takaful operator (TO), merely manages affairs of the business against a variety of financial incentives. Premiums collected by Tos are therefore, in principle, owned by the policyholders as a group and so is any surplus or deficit from the insurance operation. Participants in this case insure one another on a non-profit basis and make contributions to the takaful pool on the basis of tabarru' conditional and irrevocable donation) which is a non-commutative contract. Tel: 011947535%. E- mail address likhan trobe.edu.au Conventional insurance, mutual or otherwise, is argued to have elements of riba (which includes interest and any payment over and above the premium and gharar (uscertainty that resembles gambling, the rules of ribe and gharat do not apply to non-commutative contracts Contributions to takeful pool are therefore treated as seborre to get around the problem of ribe and share. See Archer et al. (2009). Bakat 2009 and Camal 2006 Intepix.de.org/10.10160,201411001 0167-2681/0 2014 Elsevier BV All rights reserved Han Journal of Economic Devir Gr Organisation 109 (207572-16 As is obvious, the relationship between the policyholders and a TO is that of a principal and an agent in the well-known agency problem where the agent (TO) may not work in the best interest of the principal (policyholders. In this context. optimal contracting focusses on designing incentive schemes that induce the agent to work in the best interest of the principal (see Mas-Colell et al. 1995, Chapter 14). A related aspect is that since regulators have the responsibility and mandate to safeguard the best interests of the contracting parties, optimal incentives reduce the burden of surveillance on regulators. This paper analyses the incentive schemes offered to TOs primarily to understand the power of these incentives in mitigating the agency problem so that the interest of all parties (policyholders, operators and regulatoes) are served. This sort of analysis is viewed as a powerful tool and is frequently applied to real-world scenaries (see for example Base and Bhatti, 2013: Banerjee et al. 2012; Shapiro, 2005: Bebchuk and Fried. 2003: Laffont and Martimot 2002: Eisenbart. 1989 Cooper and Hayes, 1987). An additional significance of this exercise for the Islamic insurance industry in particular is that in practice, the poli- cyholders do not have any direct or indirect input in the selection and design of these incentive schemes, which adds to the severity of the agency problem and shifts the responsibility to the regulators. Most regulators, however, do not have well-defined incentive-related guidelines, making them ill-equipped to deal with the agency problem and the analysis in this paper even more relevant. Much of the focus until now has been on regulatory issues common between conventional and Islamic insurance with little attention to the design of incentive schemes. This paper will hopefully assist regulators in understanding the role of incentives in the Islamic insurance industry and in reducing problems associated with the principal-agent relationship. The analysis in this paper corresponds to a scenario where policyholders as a group. delegate regulators the right to design the incentive schemes on their behall. The group of policyholders is therefore modelled as a single entity. The contribution of this paper is novel in the sense that it applies standard tools of optimal contracting to the operations of Islamic insurance, which to the best of our knowledge is the first attempt of its kind, and identifies the value addition of hybrid contracting when the agent's management sole can be bifurcated into sub-tasks The rest of the paper is organised as follow. Section 2 starts with an introduction of alternative incentive schemes offered to TOS.followed by a parsimonious model of optimal contracting that analyses the impact of the alternative incentive schemes on a vector of efforts exerted by the operator (Section 3) These efforts mainly include (i) admitting policyholders into the takaful pool through (ii) underwriting (selecting classifying and pricing risks) and (IM) investing a part of the premium pool technical reserves). Section 32 derives optimal values of the incentives with a view to minimise the agency problem. This section also highlights the value added of individual incentive schemes and discusses the conditions under which hybrids of the alternative schemes are beneficial. Section 4 concludes. 2. Incentives offered to takaful operators Financial incentives offered to Tos are restricted to be compliant with Islamic Law. referred to as storio. In practice, these incentives are based on an agency or wakalah contract where a TO manages takaful operations against an upfront agency fee() a mudarobah (profit sharing) contract where the TO receives a share in investment income from technical reserves, and (m) a modified udarobah (surplus-sharing) contract where the TO receives a share in insurance surplus. Most operators use a hybrid of these three incentive schemes in their operations Ina pure wakalah model, a wakalah fee is generally expressed as a percentage of the premium.collected from policyholders, and is received upfront at the time a policyholder is admitted to the takaful pool All claims and operational expenses in this case are paid from the takaful pool. The management of the takaful operation involves investment of the technical reserves and all profits or losses are credited to the takaful pool. In a pure mudarabah model on the other hand, the TO's only compensation comes out of the profits from investment of the technical reserves. The modified moderabah contract is similar to the mudarabah contract but the insurance surplus (deficit) is now treated as muderabah profit loss). This modification implies that premiums, instead of technical reserves, serve as mudarobah capital, hence the name modified muderabah contract Shari'ah compliance of the modified mudarba model has been controversial (see for example Archer et al. 2009: Bakar 2009). It is interesting to note that the modified mudarabah contract can be replaced with an arrangement where the underlying contract does not treat premiums as mudarabah capital, and where the share in surplus is treated as a reward for performance in a manner similar to a jualah or 'alah (performance fee) contract. This means that shonch compliance may sometimes mean invoking the right sharial compliant contract that closely mimics a non-compliantone The managerial function of a TO is not much different from that of a conventional insurance company. Like any con- ventional insurance company, a TO is expected to carefully underwritenisks in the process of admitting participants to the See Bend 2004 for an application of the jalah contract in the mining industry This points towards poor shora come practices in the industry. It seems that a business perspective as been going the dignofcentives more than a shariah perspective of the experts have been reluctant to resort so moe fisibile aleative verband his (the two status quo contacts) See - 2005 for a broader discussion on the coherence of contact-basecanatic 137 He When ournal of Economic choir & Orpamitation 109/2015) 135-144 takaful pool, manage claims, and invest technical reserves. The difference lies in the underlying incentives to perform these functions. This is summarised in the following basic accounting identity of the insurance operation P-COE+ITR (1) where Insurance surplus or deficit before operator's compensation: P-Net earned premium (net of reinsurance): COE-combined operating expenses: ITR-Investment income from technical reserves: COE is the sum of underwriting expenses (UE) and net claim expenses-net of reinsurance claims (NCE) Eq. (1) summarises the best interest of the contracting parties. The best interest of the party with property rights to is best served by efforts that maximise . Assuming a reasonable level of competition in the market. this requires efforts towards (1) minimisation of the COE and (ii) maximisation of OTR. Since all surpluses or deficits belong to the insurance company, a conventional insurance operator puts maximum effort in all directions. A TO, on the other hand, works for policyholders against a variety of financial incentives. These incentives may or may not induce the TO to exert maximum effort due to the agency problem which motivates our analysis in this paper. Denoting the number of policyholders by w which also represents the size of the takaful pool and the premium charged to each policyholder by "p, we can write (2) Let W be the total compensation received by the operator as a result of an incentive scheme. In a wakalah model, the operator is paid a fixed proportion fac[0,1]) of the earned premium. The compensation received by the operator in a wakalah model denoted by W., is given by WP Similarly, in a mudarabah-based model, the operator receives an agreed upon proportion (m) of the investment income from technical reserves in case of positive profits and zero otherwise. W. the compensation received in a mudaraboh model can therefore be expressed as W.TR In surplus-sharing models (modified mudarabait and ju'alah models), on the other hand, the operator receives a share ts) in the insurance surplus net of the wakulah and mudarabah compensation and nothing in case of a deficit. The compensation received in this case (W) can be expressed as W.- *-W-W. (5) A hybrid ad of the three contracts can be e written as a sum of Egs. 13)(4) and (5) so that WP + MIITR+ - WwW) In practice we observe contracts with s-0 (wakalah-mudarabah model), m=0 (modified wakalah-mudarabah model), and m-(modified mudarabah model). Using Eqs. (1) (3) and (4) we can rewrite Eq (6) as W-Is+(1-sar]P-COE +Is+(1 sm}/TR (7) 3. The model Consider a To hired by the policyholders to manage takaful operations on their behalf. The operator is offered a hybrid of incentives summarised by Eq. (6). In return the operator is expected to exert a vector of costly efforts (admitting participants into the takaful pool through carefully underwriting risks and investing the technical reserves). The underwriting effort involves selection (examining, accepting or rejecting risks) classification of the participants selected into relevant categories such as low, medium or high risk) and pricing (choosing an appropriate premium for each classification) Letc be the average claim when underwriting effort is minimum (normalised to zero here) and is the underwriting effort exerted by the operator that can be interpreted as the average time spent, over and above the minimum level, on screening policyholders before admitting them to the takaful group. Since careful underwriting reduces the chances of 16 Since is increasing in premium, this assumption discourages overpricing which is against the best interest of the policyholders. Since overpricing is best resolved by competition, we abstract away from incentive structures any that may resolve the overpricing problem Wakalah fee here sumed to be a fixed proportion of the net earned premium. In practice, however, it is expressed as a proportion of gross samed premium (CEP) This does not make any difference as far as evaluating Incentive schemes is concerned. For a given value of neurance expenses as a percentage of Art and premium) it is trivial to work out that wallah fee as a proportion of EP will be equal to a Alternatively, one could think of the wakalah fee as a percentage of GEP and add the insurance expenses to the COE The results of the paper bold in any case Note that in the modernah and surplus-sharing contracts, the agent receives a sure in profit plus and all lies are borne by policyholders as a group. This is effectively a limited liability constant. We ignore the limited liability constraints for simplicity as they do not change the qualitative results derived in this paper. This is further discussed in Section (19) 1. Khan Journal of Economihor Organisation 108/2015 125-144 139 3.1. Operator's optimisation The operator optimally chooses n. c. and k to maximise U. (E9 (15)) subject to the participation constraint. The partici- pation constraint requires that the utility of the operator from incentives offered by policyholders must not be lower than her outside option (normalised to zero here), ie, Ux20 which gives EW12C+ Te is straightforward to show that the first order conditions (FOCs) for the operators optimisation give (see Appendix A for proof) (1 - 5yapp-) (20) nesu (21) I Is +(1-5) mi (22) The solution above indicates that a pure wakalah model (cr>0 and m-5-0) motivates the operator to increase the size of the pie, but gives it no incentives to exert more than the minimum level of effort in underwriting risks or investing technical reserves. This is because underwriting effort and investment income from technical reserves do not increase its payoff. For the same reason, in a pure mudarabah model (m> and r-5-0). the operator does not have any incentive to increase the size of the pic or exert greater than the minimum level of underwriting effort. In a pure surplus-sharing model (s > and G#m-0), the operator has some incentives to exert greater than the minimum level of effort in all directions as her payoff in this case is increasing in the size of the pie, underwriting effort and investment income from technical reserves. The following highlights some important results in the context of hybrid contracts I. n is increasing in wakalah fee as and=(1-spic, >. The effect is, however, reduced by the degree of surplus-sharing Intuitively, surplus-sharing crowds out the effect of wakalah incentives because it allows the operator to recover part of the premium from the surplus and also because part of the premium is paid out in claims. In the absence of wakalah n-s(p-c) and anas-p-p>0. Surplus-sharing therefore induces the agent to increase the number of policyhold- ers as it increases payoff of the operator. In general, anas-(1-ap-only whena 0 and m-5-0) motivates the operator to increase the size of the pie, but gives it no incentives to exert more than the minimum level of effort in underwriting risks or investing technical reserves. This is because underwriting effort and investment income from technical reserves do not increase its payoff. For the same reason, in a pure mudarabah model (m>0 and 5-0), the operator does not have any incentive to increase the size of the pie or exert greater than the minimum level of underwriting effort. In a pure surplus-sharing model (s> and crm-0. the operator has some incentives to exert greater than the minimum level of effort in all directions as her payoff in this case is increasing in the size of the pie, underwriting effort and investment income from technical reserves. The following highlights some important results in the context of hybrid contracts 1. is increasing in wakalah fee as aulau-(1-5)p>0. The effect is, however, reduced by the degree of surplus-sharing Intuitively, surplus-sharing crowds out the effect of wakalah incentives because it allows the operator to recover part of the premium from the surplus and also because part of the premium is paid out in claims. In the absence of wakalah -sp-C) and anas-p-c>0.Surplus-sharing therefore induces the agent to increase the number of policyhold- ers as it increases payoff of the operator. In general, anas=((1-ap-c>Donly whene) which cancels out the impact of surplus-sharing on the optimal size of the pool in the presence of wakalah incentives. We also show that the optimal size of the pool ina wakalah model without surplus-sharing (a) is greater than optimal size of the pool in a surplus-sharing model and its hybrid with mudarobah) and (b) equal to the optimal size in any wakalah hybrid model. This means that wakalah outperforms surplus-sharing models in terms of increasing the size of the pool and is a better alternative it. The underwriting effort, on the other hand, is solely motivated by surplus-sharing Wakoloh and mudaraboh incentives do not have any direct effect on the underwriting effort. The indirect effect may feed through its impact ons, which is discussed later iiiInvestment of the reserves, on the other hand, is increasing in both mands as al-(1-5) and alas-1-m). The level of these effects is also partially crowded out by surplus-sharing and muderabah hybrids respectively. This is because part of the investment income is received by the operator through surplus-sharing (which reduces the attractiveness of mudarabah) and because distributable surplus is decreasing in muderabah share (which reduces the effectiveness of surplus-sharing in the presence of mudarabah). 3.2. Policyholders" choice of incentives Whereas the agent treats incentive parameters (a. mand s) as exogenous, the principal has the option of choosing them optimally. The principal chooses these incentives such that it maximises U(Eq. (14)) subject to the agent's participation constraint given by Eq. (19) and the agents optimal choice of ne, and k (implied by Eq. (20) .211 and 22. respectively Assuming as the base case and substituting these constraints into Eq. (14) reduces the objective function to U, P C + suv? Low?- }s + (1 - bumper (23) The FOCS WI..., m and simply the following 1 (24) -- (0 -skapasip. (0-5)-200 -skap + sip -->1 +15+(1-sympa 7/07 15+ (1-5) Plo (1 + (F/007) 1s+(1-5) (25) (1 + (P/do?)) (26 140 H. Khan/Soumal of Economie Bio Organbation 08 (2015135-144 12/02 (1 + (2/6) Substituting Eq. (26) in (25) gives (1/60) - (02/007) when 1 + (1/60) ma when (27 0 where i/ho, is a measure of risk-adjusted return on investment and u/vore is a similar measure of risk-adjusted retur on underwriting effort (formally known as Sharpe ratios) The correspondence between Eqs. (24)-(26) and the optimal size of the pool (n"), underwriting effort (ex") and investmen !' is obvious. It is however important to highlight the difference in the optimal size in models with and without wakala incentives. This difference is summarised as follows 5.(P-C) when 0 (28 (p-C) when a > 0 Cp Let us now state the main results 1. All incentives offered to TOs must include surplus-sharing as s'>0 (as it motivates effort in all directions), ii. A wakalah hybrid should be offered only when minimum effort is profitable (when average claim with minimum effor is less than the average premium, ie,c

0 when i/o?+0) >/? +0x) (se Appendix A for proof) vi. When the risk-adjusted return on investment increases, it is optimal to increase reliance on madarabahwithout reducing reliance on surplus-sharing when $.fc)-0 as am 1 a(P/00) 1+P/407 es. i 2 0 141 Hi han fournel of Economic Behavice & Organito 209/2015, 135-144 However, when Etc.) +0, as"facf} 16) which implies substitution between the two when the risk-adjusted return on investment increases. Intuitively, this is because an increase in (f/4?) reduces the impact of unexpected variations on investment income relative to their impact on underwriting effort vii. Unexpected variations in claims seduce investment of technical reserves as they negatively correlate with investment income. This means the operator holds more reserves in its stock to finance any unexpected claims. To show this, we substitute Eq. (25) in (22) to get (29) de Using the extended solution in Appendix A, we can show that P-1,5 (30) + do? A comparison of Eqs. (29) and (30) confirms our conjecture as " [^-skup * *2-0) 2.0 - sp +*+p+ oFP ++8+41 - smtp show) 14 am H. Khan/Jounal of Economic Behavior Organisation 109(2005) 735-14 The FOCs for the principal's optimisation problem are as follows au (1 - -- (1-5 P01 sop+50-0) - au, (t-sXP-sc) - (1 - 3) + (1 -mc +00%) - 0 au, -" +(1 - m)|s+ (1 - symP+007)-(-s) - $(" + do?) -Is+ (1 - 0 Simplifying the Focs gives us a) is (A4) 13+ (1 -m - (AS) Is +(1-5) + (A6) Solving Eas.(AS) and (A6) further gives IP/(?)-(w/o+0) (A7) Cofoco +oXo +00))+ (P/Cap) - Cop/d+oXo+px)} (UP/007)//(1+(f/60*XXX/07) (AS) (1 +(u?/60-1 (doc/6 + (P/4000/002 As is obvious from (A7), a mudarbah hybrid is optimal only when the risk-adjusted return on investment is greater than the risk-adjusted return on underwriting effort, ie (F/dg+0) > Bloco +)). This is similar to our base case model. Risk in this case is however adjusted for the covariance effect Furthermore, it is straight forward to show that the partial effects discussed in the base case have the same sign in the extended case (Ele) 30) (2 +00/XP+o)-() am. (1 -m , ase >0 A) P.) (1-5) +607) ame Is +(1-5 do +1 (de) (1-5) [(1 - 5)(P+def 1 do ie + (1 -m) 0 Wood) -3) (P+dos des (A13) lo o when i? /60?> /do?. Moreover, the solution implies m /(P2 / ba?) > 0 am - /au/002) O like the base case model. The principal's degree of risk aversion therefore does not change the qualitative results of the base case model. References Akerlof, G.A. 1982. Labor contracts as partial gift exchange0. J. Econ.97(4.). 543-569 Archer, S. Karim, R.A., Nienhaus, V. 2009. Business models in takaful and regulatory implication. In: Archer, S. Karim, RA, Nienhaus, V. (Eds.). Takaful Islamic Insurance Concepts and Regulatory issues. John Wiley and Sons (Assa) Singapore. pp. 9-30 Bakar, D.M. 2009. Shari'ah principles governing takaful models. In: Archer, S. Karim, RA. Nienhaus. V. (Eds.). Takaful Islamic Insurance Concepts and Regulatory Issues. John Wiley and Sons (Asia), Singapore, pp 31-45. Banerjee, B.M., Dutta, S., Ray.S. 2012. Applications of agency theory in B2B marketing review and future directions, Inc Lilien, G.Grewal, R. (Eds.), Handbook of Business-to-Business Marketing Edward Elgar Publishing. Cheltenham, pp. 41-53 Basov, S., Bhatti, M., 2013. Optimal contracting model in a social environment and trust-related psychological costs. HEJ. Theor. Econ. 13.271-284. BebchukLA. Bendjilal, B. 2004. The Ja'ala contract and its applicability to the mining sector. Discussion Paper No. 14. blamic Research and Training Institute, Islamic Development Bank, jeddah. BNM/RH/GL. 004-22. Guidelines on Takaful Operational Framework. Bank Negara Malaysia Cooper, R., Hayes, B., 1987. Multi-period insurance contracts, Int. J. Ind. Org 5.211-231 Eisenhardt, M.K., 1989. Agency theory: an assessment and review. Acad. Manage Rex: 14(1):55-74 EL-Gamal , M., 2006. A Simple Figh-and-Economics Rationale for Mutualisation in Islamic Financial Intermediation. The Rice University, Houston, Retrieved March 01, 2014 from http://www.rubrice.edul-elgamal/files/mutualize.pdf El-Gamal, M. 2008. Incoherence of contract based Islamic financial jurisprudence in the age of financial engineering Wis. Int Law J. 25 (4.). 605-623. Englmaier, E. Leider, S. 2012. Contractual and organisational structure with reciprocal agents. Am. Econ. J. Microecon. 4. 146-183. Laffont. J. Martimort, M. 2002. The Theory of Incentives: The Principal-Agent Model Princeton University Press, Princeton. Mas-Colell, A., Whinston, M.D. Green. J.R., 1995. Microeconomic Theory. Oxford University Press, New York Shapiro, S.P. 2005. Agency theory. Annu. Rev. Sociol. 31,263-284