Kostakis et al. (2011, show Section 2) that marginal rate of substitution of wealth can be approximated by a function of the first three moments of asset returns and the agent's relative risk aversion (Arrow, 1964; Pratt, 1964), relative prudence (Kimball, 1990) and relative temperance (Eeckhoudt et al. 1996).

(a) Define and study the three measures of preference function, i.e. risk aversion, prudence and temperance.

(b) What are the relative risk aversion, relative prudence and relative temperance of an investor who has a power utility of the same form in Merton's CRRA investor?

(c) What are the relative risk aversion, relative prudence and relative temperance of an investor who has a HARA utility?

(d) What are the relationships between these three measures of preference function and asset return risk premium?

(e) How is jump impact on the first three moments of asset returns? How would the risk premium of jumps change extending from your answers to part (d)? (Kostakis et al. 2011).