Abstract
In this paper, the optimal investment problem for an agent with dual risk model is studied. The financial market is assumed to be a diffusion process with the coefficients modulated by an external process, which is specified by the solution to a kind of stochastic differential equation. The object of the agent is to maximize the expected utility from terminal wealth. Together with the regularity property of the value function, by dynamic programming principle, the value function of our control problem is turned to be the unique solution to the associated Hamilton-Jacob-Bellman (HJB for short) equation. When the utility is an exponential function with constant risk aversion, close form expressions for value function and optimal investment policy are obtained.
Highlights
IntroductionI =1 where x > 0 is the initial surplus, c is the positive constant premium income rate, Nt is Poisson process with parameter λ , which denotes the total number of claims up to time t
The classical surplus process of an insurer is given by NtUt =x + ct − ∑Yi, (1)i =1 where x > 0 is the initial surplus, c is the positive constant premium income rate, Nt is Poisson process with parameter λ, which denotes the total number of claims up to time t
More details about the surplus process can be found in Asmussen and Albrecher [1], Rolski et al [2]
Summary
I =1 where x > 0 is the initial surplus, c is the positive constant premium income rate, Nt is Poisson process with parameter λ , which denotes the total number of claims up to time t. (2015) Optimal Investment under Dual Risk Model and Markov Modulated Financial Market. To our best knowledge, there are few papers concentrate on the optimal investment of agent with dual risk process. This is the main contributions of this paper. Among all kinds of stochastic coefficients models, Markov-modulated risky model has been recognized recently as an important feature to asset price models. The optimal investment problem of an agent with dual risk process under the Markov modulated financial market is studied. A solid example is presented to illustrate how to solve the HJB equation when the claims are exponential distribution This rest of this paper is organized as follows.
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