Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer in a Competitive Market

28 Pages Posted: 19 Jul 2011

See all articles by Krzysztof Ostaszewski

Krzysztof Ostaszewski

Illinois State University

Hong Mao

Shanghai Second Polytechnic University

Date Written: June 22, 2011

Abstract

In this article, we establish a model of insurance pricing with the assumptions that the insurance price, investment returns and insured losses are correlated stochastic processes, while also considering the affect of the demand on the price. The objective of the pricing model is to maximize the expected utility of the terminal wealth of an insurer. We construct a Hamilton–Jacobi–Bellman (HJB) equation and determine the optimal price of an insurance product and optimal investment portfolio of an insurer simultaneously by solving that HJB equation. We also carry out sensitivity analysis. The results of our analysis show that elasticity of insurance demand greatly affects the optimal solutions. Notably, quantity of insurance demanded affects the optimal allocation to risky assets in the insurer’s investment portfolio. Therefore, the demand function for insurance must be considered in management of insurance firm. Our results also show that the drift and volatility of the process of insurance price will affect the investment strategy, in addition to the effect of the drift and volatility of investment process itself. Finally, the drift and volatility of investment stochastic process will affect the insurance price in the cases when the elasticity of demand is large, but that influence is negligible with small elasticity of demand.

Suggested Citation

Ostaszewski, Krzysztof and Mao, Hong, Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer in a Competitive Market (June 22, 2011). Available at SSRN: https://ssrn.com/abstract=1888013 or http://dx.doi.org/10.2139/ssrn.1888013

Krzysztof Ostaszewski (Contact Author)

Illinois State University ( email )

Department of Mathematics
Normal, IL 61790-4520
United States
+1-309-438-7226 (Phone)
+1-309-438-5866 (Fax)

HOME PAGE: http://math.illinoisstate.edu/krzysio

Hong Mao

Shanghai Second Polytechnic University ( email )

No.2360, Jinhai Road
Shanghai, 201209
China

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