Optimal investment, consumption and proportional reinsurance for an insurer with option type payoff

Exponential utility maximization for an insurer with time-inconsistent preferences

“…This confirms the well-known fact that the timeconsistent equilibrium strategy for exponential discount function is nothing but the optimal strategy. Since there is a mistake in the result of Peng et al (2014b) 4 , we do not compare our result with theirs, though their model is more closer to ours. Since the time-consistent investment strategy and reinsurance strategy are the same for nonexponential and exponential discount functions, we only compare the consumption strategies.…”

“…The proof of the above result is similar to Peng et al (2014b), which originates from Hu et al (2005) and Cheridito and Hu (2011), and we omit the details here. The idea is to prove that the process…”

“…With exponential discount function, the optimal consumption strategy consists of a proportion (given by g(·)) of the wealth and an adjustment term, see Cheridito and Hu (2011) and Peng et al (2014b). In this paper, to show the effect of the non-exponential discount function, we decompose the adjustment term into two parts.…”

“…The object is to maximize the utility of intertemporal consumption and terminal wealth. The model is similar to the one adopted in Peng et al (2014b), where the insurance risk and financial risk are independent. Since the insurer's surplus may be affected by the performance of the financial market, we consider the dependence between the insurance risk and financial risk.…”

“…2 Similar toCheridito and Hu (2011) andPeng et al (2014b), we may also consider a general constraint on the investment strategy. In this paper, for simplicity and focusing on the time-inconsistency, we only consider the constraint on the reinsurance strategy.…”