Mean-variance portfolio selection for a non-life insurance company

被引：0
作者：
Łukasz Delong
Russell Gerrard
机构：
[1] Warsaw School of Economics,Institute of Econometrics, Division of Probabilistic Methods
[2] Cass Business School,Faculty of Actuarial Science and Insurance
来源：
Mathematical Methods of Operations Research | 2007年 / 66卷
关键词：
Lévy diffusion financial market; Compound Cox claim process; Hamilton–Jacobi–Bellman equation; Feynman–Kac representation; Efficient frontier;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise. We investigate two optimization problems. The first one is the classical mean-variance portfolio selection. In this case the efficient frontier is derived. The second optimization problem, except the mean-variance terminal objective, includes also a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target which is a random process. In order to find optimal strategies we apply techniques from the stochastic control theory.
引用
收藏
页码：339 / 367
页数：28
相关论文
共 39 条
  • [1] Bäuerle N(2005)Benchmark and mean-variance problems for insurer Math Methods Oper Res 62 159-165
  • [2] Becherer D(2005)Classical solutions to reaction-diffusion systems for hedging problems with interacting Itô processes Ann Appl Probab 15 1111-1144
  • [3] Schweizer M(2005)Dynamic mean-variance with portfolio selection with bankruptcy prohibition Math Finance 15 213-244
  • [4] Bielecki T(2004)Wealth-path dependent utility maximization in incomplete financial markets Finance Stoch 8 579-603
  • [5] Jin H(1995)Optimal investment policies for a firm with a random risk process: exponential utility and minimizing probability of ruin Math Oper Res 20 937-958
  • [6] Pliska S(2006)Portfolio optimization in stochastic markets Math Meth Oper Res 63 151-168
  • [7] Zhou XY(2006)Kalman-Bucy filtering for linear systems driven by the Cox process with shot noise intensity and its applications to the pricing of reinsurance contracts J Appl Probab 42 93-107
  • [8] Bouchard B(2005)Optimal investment strategy for a non-life insurance company: quadratic loss Appl Math 32 263-277
  • [9] Pham H(2004)Investment choices post retirement in a defined contribution pension scheme Insur Math Econ 35 321-342
  • [10] Browne S(2004)Optimal portfolio selection when stock prices follow a jump-diffusion process Math Methods Oper Res 60 485-496
1234