Overview

Vincentian Auto Insurance Co$.$ has hired your team and six other teams to help the pricing actuary determine an appropriate premium rate, effective $\frac{1}{1}\frac{?}{2025}.$

You are expected to present your findings in person on Friday. A team leader that has been assigned to your team will be assisting you with your work.

Discussion of project

To forecast future cash flows and come up with a suitable premium rate, the company will need estimates of the following:

Number of new policies issued

Number of existing policies $($in$-$force$)$ larr From accounting team

Persistency $(\%$ of existing policies that get renewed$)$

Loss claims

Incurred but not reported losses

Expenses larr From operation team

Investment income larr From investment team

Your team will be in charge of estimating number of new policies. The other teams will tackle the remaining aspects of this project. You are also provided with monthly data on new policies from the ten most recent years.

Assumptions

Annual productivity gains of $2\%$ should be incorporated in your estimates.

No other economic adjustments should be considered.Analysis

Your analysis should address the following questions:

i$.$ Is the data reasonable? Any potential outliers that should be examined further?

ii$.$ Is there seasonality in the data?

iii. Is there a trend in year$-$over$-$year number of new policies, after applying the indicated economic adjustment?

If your answer to part iii. is yes, then this trend should be taken into account when estimating the number of new policies for $2025.$

iv$.$ What is the expected $($mean$)$ number of new policies for $2025?$

v$.$ What is the standard deviation of the number of new policies?

vi$.$ What is the number of new policies corresponding to the ${95}^{th}$ percentile of the distribution?

Part vi$.$ is commonly referred to as VaR at $95\%.$ It represents a sufficiently$-$adverse$-$yet$-$possible outcome for new policies issued $($make sure you have ordered your simulation data from most to least favorable$).$ You are encouraged to compute VaR at $95\%$ in more than one way.

vii. Illustrate visually the range of all possible future outcomes and their likelihood, in terms of a histogram.

viii. Identify the points of the graph corresponding to the expected number of new policies and the VaR $95\%.\backslash$table$[[$VINCENTIAN AUTO IN$URANCE C $.],[$Number of new policies issued $($in thousands$)],[,$January,February,March,April,May,June,$|$July$,$August,September,October,November,December$],[2014,$no data,$6\mathrm{.}423,6\mathrm{.}547,\frac{?}{\text{b}\text{a}\text{r}}(6\mathrm{.}108),\frac{?}{\text{b}\text{a}\text{r}}(5\mathrm{.}928),5\mathrm{.}532,4\mathrm{.}937],[2015,5\mathrm{.}076,4\mathrm{.}437,5\mathrm{.}432,5\mathrm{.}833,6\mathrm{.}283,6\mathrm{.}506,6\mathrm{.}78,6\mathrm{.}423,6\mathrm{.}297,5\mathrm{.}937,5\mathrm{.}406,5\mathrm{.}63],[2016,4\mathrm{.}912,4\mathrm{.}594,5\mathrm{.}487,5\mathrm{.}94,6\mathrm{.}228,3\mathrm{.}987,5\mathrm{.}571,6\mathrm{.}885,9\mathrm{.}282,6\mathrm{.}202,4\mathrm{.}92,,5\mathrm{.}237],[2017,5\mathrm{.}665,5\mathrm{.}307,5\mathrm{.}78,6\mathrm{.}124,6\mathrm{.}996,6\mathrm{.}81,5\mathrm{.}809,7\mathrm{.}181,5\mathrm{.}489,6\mathrm{.}52,5\mathrm{.}939,5\mathrm{.}125],[2018,5\mathrm{.}29,4\mathrm{.}747,5\mathrm{.}913,6\mathrm{.}405,6\mathrm{.}626,7\mathrm{.}173,7\mathrm{.}36,7\mathrm{.}66,6\mathrm{.}653,6\mathrm{.}495,6\mathrm{.}326,5\mathrm{.}122],[2020,5\mathrm{.}583,5\mathrm{.}148,6\mathrm{.}303,6\mathrm{.}513,6\mathrm{.}977,7\mathrm{.}232,7\mathrm{.}499,7\mathrm{.}695,6\mathrm{.}825,5\mathrm{.}928,6\mathrm{.}138,5\mathrm{.}879],[2021,10\mathrm{.}252,5\mathrm{.}69,5\mathrm{.}2,6\mathrm{.}398,7\mathrm{.}183,7\mathrm{.}394,8\mathrm{.}136,7\mathrm{.}335,6\mathrm{.}712,6\mathrm{.}82,6\mathrm{.}339,5\mathrm{.}868],[2022,5\mathrm{.}793,5\mathrm{.}443,6\mathrm{.}273,7\mathrm{.}108,7\mathrm{.}32,7\mathrm{.}503,7\mathrm{.}403,7\mathrm{.}491,7\mathrm{.}522,7\mathrm{.}282,6\mathrm{.}896,\backslash$table$[[5\mathrm{.}703]]],[2023,5\mathrm{.}836,10\mathrm{.}282,6\mathrm{.}454,6\mathrm{.}843,7\mathrm{.}304,8\mathrm{.}564,7\mathrm{.}737,12\mathrm{.}039,3\mathrm{.}082,7\mathrm{.}139,7\mathrm{.}028,9\mathrm{.}997],[2024,6\mathrm{.}035,5\mathrm{.}341,9\mathrm{.}256,7\mathrm{.}002,7\mathrm{.}562,12\mathrm{.}038,$no data$]]$