Abstract
In this paper, we consider an insurer who wants to maximize its expected utility of terminal wealth by selecting optimal investment and risk control strategies. The insurer’s risk process is modeled by a jump-diffusion process and is negatively correlated with the returns of securities and derivatives in the financial market. In the financial model, a part of insurers’ wealth is invested into the financial market. Using a martingale approach, we obtain an explicit solution of optimal strategy for the insurer under logarithmic utility function.
Highlights
In the past two decades, more and more attention has been paid to the problem of optimal investment in financial markets for an insurer
The insurer’s risk process obeys a jump-diffusion process, and it is not total its capital to invest but a part of wealth to invest in financial market
We consider that an insurer wants to maximize its expected utility of terminal wealth by selecting optimal control
Summary
In the past two decades, more and more attention has been paid to the problem of optimal investment in financial markets for an insurer. Based on the Merton’s work, Zhou and Yin (2004) [2], and Sotomayor and Cadenillas (2009) [3] considered consumption/investment problem in a financial market with regime switching. Wang process to Merton’s model, such as Yang and Zhang (2005) [6] They considered stochastic control problem for optimal investment strategy without consumption under a certain criteria. Based on the limiting process of compound Poisson process, Taksar (2000) [7] wrote the paper about optimal risk and dividend distribution control Following his same vein, recent researches started to model the risk by diffusion process or a jump-diffusion process; see, e.g. Wang (2007) [8] and Zou (2014) [9].
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