基于易腐品和不可分割耐用品的最优消费投资与寿险购买策略
|
摘要
随着经济的发展和人民生活水平的提高,投资者的投资组合不再局限于证券市场投资.通过将寿险购买引入投资者的投资组合并划分消费品为易腐品或不可分割耐用品,研究投资者的最优消费投资与寿险购买策略.投资者的投资目标为期望效用最大化.运用动态规划原理得到哈密尔顿-雅可比-贝尔曼方程,最终得到最优策略满足的方程,并讨论方程存在正根的条件.最后通过数值分析方法,验证模型结论与实际现实情况的一致性.
With the development of economy and the improvement of people's living standard, the investor's investment is no longer limited to the portfolio of the financial assets. This paper studies optimal consumption, investment and insurance purchase strategies by introducing the insurance purchase into the portfolio of the investor and dividing consumption into the perishable good or the indivisible durable good. The investor's objective is the maximum of expected utility. By using the theory of dynamic programming, the Hamilton-Jacobi-Bellman equation is obtained, the equation of existence of the optimal strategy is derived, and the condition of the positive root satisfying the equation is discussed. Finally a numerial analysis verifies that the conclusion of the proposed model fits the empirical behavior in reality.
With the development of economy and the improvement of people's living standard, the investor's investment is no longer limited to the portfolio of the financial assets. This paper studies optimal consumption, investment and insurance purchase strategies by introducing the insurance purchase into the portfolio of the investor and dividing consumption into the perishable good or the indivisible durable good. The investor's objective is the maximum of expected utility. By using the theory of dynamic programming, the Hamilton-Jacobi-Bellman equation is obtained, the equation of existence of the optimal strategy is derived, and the condition of the positive root satisfying the equation is discussed. Finally a numerial analysis verifies that the conclusion of the proposed model fits the empirical behavior in reality.
引文
[1] Merton R C. Optimum consumption and portfolio rules in a continuous-time model[J]. J of Economic Theory,1971, 3(4):373-413.
[2] Song J, Bi X, Li R, et al. Optimal consumption and portfolio selection problems under loss aversion with downside consumption constraints[J]. Applied Mathematics&Computation, 2017, 299:80-94.
[3] Chang H, Chang K. Optimal consumption–investment strategy under the Vasicek model:HARA utility and Legendre transform[J]. Insurance:Mathematics&Economics, 2017, 72:215-227.
[4] Vasicek Oldrich. An equilibrium characterization of the term structure[J]. J of Financial Economics, 1977, 5(2):177-188.
[5] Wang G, Wang X, Zhou K. Pricing vulnerable options with stochastic volatility[J]. Physica A:Statistical Mechanics&Its Applications, 2017, 485:91-103.
[6] Chang Hao. Optimal investment and consumption decisions under the constant elasticity of variance model[J]. Mathematical Problems in Engineering, 2013,2013(1):1-11.
[7] Kwak M, Lim B H. Optimal portfolio selection with life insurance under inflation risk[J]. J of Banking&Finance,2014, 46(3):59-71.
[8] Ma Qinghua, Yi Fahuai, Guan Chonghu. A consumption–investment problem with constraints on minimum and maximum consumption rates[J]. J of Computational and Applied Mathematics, 2018, 338:185-198.
[9] Liu C, Zheng H. Asymptotic analysis for target asset portfolio allocation with small transaction costs[J].Insurance:Mathematics&Economics, 2016, 66:59-68.
[10] Frutos J D, Gatón V. A spectral method for an optimal investment problem with transaction costs under potential utility[J]. J of Computational&Applied Mathematics,2017, 319:262-276.
[11] Pliska S R, Ye J. Optimal life insurance purchase and consumption/investment under uncertain lifetime[J]. J of Banking&Finance, 2007, 31(5):1307-1319.
[12] Duarte I, Pinheiro D, Pinto A A, et al. Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms[J]. Optimization, 2014, 63(11):1737-1760.
[13] Han N W, Hung M W. Optimal consumption, portfolio,and life insurance policies under interest rate and inflation risks[J]. Insurance:Mathematics&Economics, 2017, 73:54-67.
[14] Domenico Cuoco. Optimal consumption of a divisible durable good[J]. J of Economic Dynamics&Control,2000, 24(4):561-613.
[15] Anders Damgaarda. Optimal consumption and investment strategies with a perishable and an indivisible durable consumption good[J]. J of Economic Dynamics&Control, 2004, 28(2):209-253.
[2] Song J, Bi X, Li R, et al. Optimal consumption and portfolio selection problems under loss aversion with downside consumption constraints[J]. Applied Mathematics&Computation, 2017, 299:80-94.
[3] Chang H, Chang K. Optimal consumption–investment strategy under the Vasicek model:HARA utility and Legendre transform[J]. Insurance:Mathematics&Economics, 2017, 72:215-227.
[4] Vasicek Oldrich. An equilibrium characterization of the term structure[J]. J of Financial Economics, 1977, 5(2):177-188.
[5] Wang G, Wang X, Zhou K. Pricing vulnerable options with stochastic volatility[J]. Physica A:Statistical Mechanics&Its Applications, 2017, 485:91-103.
[6] Chang Hao. Optimal investment and consumption decisions under the constant elasticity of variance model[J]. Mathematical Problems in Engineering, 2013,2013(1):1-11.
[7] Kwak M, Lim B H. Optimal portfolio selection with life insurance under inflation risk[J]. J of Banking&Finance,2014, 46(3):59-71.
[8] Ma Qinghua, Yi Fahuai, Guan Chonghu. A consumption–investment problem with constraints on minimum and maximum consumption rates[J]. J of Computational and Applied Mathematics, 2018, 338:185-198.
[9] Liu C, Zheng H. Asymptotic analysis for target asset portfolio allocation with small transaction costs[J].Insurance:Mathematics&Economics, 2016, 66:59-68.
[10] Frutos J D, Gatón V. A spectral method for an optimal investment problem with transaction costs under potential utility[J]. J of Computational&Applied Mathematics,2017, 319:262-276.
[11] Pliska S R, Ye J. Optimal life insurance purchase and consumption/investment under uncertain lifetime[J]. J of Banking&Finance, 2007, 31(5):1307-1319.
[12] Duarte I, Pinheiro D, Pinto A A, et al. Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms[J]. Optimization, 2014, 63(11):1737-1760.
[13] Han N W, Hung M W. Optimal consumption, portfolio,and life insurance policies under interest rate and inflation risks[J]. Insurance:Mathematics&Economics, 2017, 73:54-67.
[14] Domenico Cuoco. Optimal consumption of a divisible durable good[J]. J of Economic Dynamics&Control,2000, 24(4):561-613.
[15] Anders Damgaarda. Optimal consumption and investment strategies with a perishable and an indivisible durable consumption good[J]. J of Economic Dynamics&Control, 2004, 28(2):209-253.