Economics - Research Publications

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    Optimal investment, consumption, and life insurance strategies under a mutual-exciting contagious market
    Liu, G ; Jin, Z ; Li, S (ELSEVIER, 2021-11)
    We study an optimisation problem of a household under a contagious financial market. The market consists of a risk-free asset, multiple risky assets and a life insurance product. The clustering effect of the market is modelled by mutual-excitation Hawkes processes where the jump intensity of one risky asset depends on both the jump path of itself and the jump paths of other risky assets in the market. The labor income is generated by a diffusion process which can cover the Ornstein-Uhlenbeck (OU) process and the Cox-Ingersoll-Ross (CIR) model. The goal of the household is to maximise the expected utilities from both the instantaneous consumption and the terminal wealth if he survives up to a fixed retirement date. Otherwise, a lump-sum heritage will be paid. The mortality rate is modelled by a linear combination of exponential distributions. We obtain the optimal strategies through the dynamic programming principle and develop an iterative scheme to solve the value function numerically. We also provide the proof of convergence of the iterative method. Finally, we present a numerical example to demonstrate the impact of key parameters on the optimal strategies.
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    Household Lifetime Strategies under a Self-Contagious Market
    Liu, G ; Jin, Z ; Li, S (Elsevier, 2021-02-01)
    In this paper, we consider the optimal strategies in asset allocation, consumption, and life insurance for a household with an exogenous stochastic income under a self-contagious market which is modeled by bivariate self-exciting Hawkes jump processes. By using the Hawkes process, jump intensities of the risky asset depend on the history path of that asset. In addition to the financial risk, the household is also subject to an uncertain lifetime and a fixed retirement date. A lump-sum payment will be paid as a heritage, if the wage earner dies before the retirement date. Under the dynamic programming principle, explicit solutions of the optimal controls are obtained when asset prices follow special jump distributions. For more general cases, we apply the Feynman–Kac formula and develop an iterative numerical scheme to derive the optimal strategies. We also prove the existence and uniqueness of the solution to the fixed point equation and the convergence of an iterative numerical algorithm. Numerical examples are presented to show the effect of jump intensities on the optimal controls.
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    Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model
    Zhang, J ; Chen, P ; Jin, Z ; Li, S (American Institute of Mathematical Sciences, 2021-03-01)
    This paper investigates a continuous-time mean-variance portfolio selection problem based on a log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive a sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equations (FBSDEs). An equilibrium strategy is derived by solving the system. To illustrate our result, we consider a special case where the interest rate process is described by the Vasicek model. In this case, we also derive the closed-loop equilibrium strategy through the dynamic programming approach.