Economics - Research Publications
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ItemOptimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models(Elsevier, 2020-02-01)In this paper, we consider the optimal consumption and investment strategies for households throughout their lifetime. Risks such as the illiquidity of assets, abrupt changes of market states, and lifetime uncertainty are considered. Taking the effects of heritage into account, investors are willing to limit their current consumption in exchange for greater wealth at their death, because they can take advantage of the higher expected returns of illiquid assets. Further, we model the liquidity risks in an illiquid market state by introducing frozen periods with uncertain lengths, during which investors cannot continuously rebalance their portfolios between different types of assets. In liquid market, investors can continuously remix their investment portfolios. In addition, a Markov regime-switching process is introduced to describe the changes in the market's states. Jumps, classified as either moderate or severe, are jointly investigated with liquidity risks. Explicit forms of the optimal consumption and investment strategies are developed using the dynamic programming principle. Markov chain approximation methods are adopted to obtain the value function. Numerical examples demonstrate that the liquidity of assets and market states have significant effects on optimal consumption and investment strategies in various scenarios.
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ItemOptimal investment, consumption, and life insurance strategies under a mutual-exciting contagious market(ELSEVIER, 2021-11-16)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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ItemHousehold Lifetime Strategies under a Self-Contagious Market(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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ItemInsurance fraud detection with unsupervised deep learning(WILEY, 2021-07-26)
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ItemContinuous-time mean-variance asset-liability management with stochastic interest rates and inflation risks(American Institute of Mathematical Sciences, 2020-03-01)This paper investigates a continuous-time Markowitz mean-variance asset-liability management (ALM) problem under stochastic interest rates and inflation risks. We assume that the company can invest in n +1assets: one risk-free bond and n risky stocks. The risky stock's price is governed by a geometric Brownian motion (GBM), and the uncontrollable liability follows a Brownian motion with drift, respectively. The correlation between the risky assets and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. By applying the Lagrange multiplier method and stochastic control approach, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation, which can be converted into six partial differential equations (PDEs). The closed-form solutions for these six PDEs are derived by using the homogenization approach and the variable transformation technique. Then the closed-form expressions for the efficient strategy and efficient frontier are obtained. In addition, a numerical example is presented to illustrate the results.
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ItemOpen-loop equilibrium strategy for mean-variance portfolio selection: A log-return model(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.
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ItemOPTIMAL STOP-LOSS REINSURANCE WITH JOINT UTILITY CONSTRAINTS(AMER INST MATHEMATICAL SCIENCES-AIMS, 2021-03-01)