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, 2021-11-16)
    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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    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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    The finite-time ruin probability under the compound binomial risk model
    Li, S ; Sendova, KP (SPRINGER HEIDELBERG, 2013-07-01)
    We study the compound binomial ruin model, which is considered to be the discrete analogue of the classical compound Poisson model. Our key result is a simple approach for inverting a generating function whose argument is the discount factor when we know the inverse of the same generating function, which this time has argument that is the solution to Lundberg’s equation. The main idea comes from a result in Dickson and Willmot (ASTIN Bulletin 35:45–60, 2005) who discuss the classical model. We are then able to derive the probability distribution of the time to ruin and to go beyond the results in Dickson and Willmot (ASTIN Bulletin 35:45–60, 2005) by deducing the distribution of the first hitting time of a specific level and the duration of the time when the surplus is negative. The paper contains several illustrative examples where specific claim-amount distributions are considered.
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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.
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    On the Type I multivariate zero-truncated hurdle model with applications in health insurance
    Zhang, P ; Calderin, E ; Li, S ; Wu, X (Elsevier, 2020-01-01)
    In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insurance business with various classes of policies. There are three types of zero-truncation in the multivariate setting: only records with all zeros are missing, zero counts for one or some classes are missing, or zeros are completely missing for all classes. In this paper, we focus on the first case, the so-called Type I zero-truncation, and a new multivariate zero-truncated hurdle model is developed to study it. The key idea of developing such a model is to identify a stochastic representation for the underlying random variables, which enables us to use the EM algorithm to simplify the estimation procedure. This model is used to analyze a health insurance claims dataset that contains claim counts from different categories of claims without common zero observations.
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    On the Moments and the Distribution of Aggregate Discounted Claims in a Markovian Environment
    Li, S ; Lu, Y (MDPI AG, 2018-05-23)
    This paper studies the moments and the distribution of the aggregate discounted claims (ADCs) in a Markovian environment, where the claim arrivals, claim amounts, and forces of interest (for discounting) are influenced by an underlying Markov process. Specifically, we assume that claims occur according to a Markovian arrival process (MAP). The paper shows that the vector of joint Laplace transforms of the ADC occurring in each state of the environment process by any specific time satisfies a matrix-form first-order partial differential equation, through which a recursive formula is derived for the moments of the ADC occurring in certain states (a subset). We also study two types of covariances of the ADC occurring in any two subsets of the state space and with two different time lengths. The distribution of the ADC occurring in certain states by any specific time is also investigated. Numerical results are also presented for a two-state Markov-modulated model case.
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    Analysis of some ruin-related quantities in a Markov-modulated risk model
    Li, J ; Dickson, DCM ; Li, S (Taylor, 2016)
    In this paper, we study the joint Laplace transform and probability generating function of some random quantities that occur in each environment state by the time of ruin in a Markov-modulated risk process. These quantities include the duration spent in each state, the number of claims and the aggregate amount of claims that occurred in each state by the time of ruin. Explicit formulae for the joint transforms, given the initial surplus, and the initial and terminal environment states, are expressed in terms of a matrix version of the scale function. Moments and covariances of these ruin-related quantities are obtained and numerical illustrations are presented. The joint transform of the duration spent in each state, the number of claims, and the aggregate amount of claims that occurred in each state by the time the surplus attains a certain level are also investigated.
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    Optimal reinsurance under dynamic VaR constraint
    Zhang, N ; Jin, Z ; Li, S ; Chen, P (Elsevier, 2016-11)
    This paper deals with the optimal reinsurance strategy from an insurer’s point of view. Our objective is to find the optimal policy that maximises the insurer’s survival probability. To meet the requirement of regulators and provide a tool to risk management, we introduce the dynamic version of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR) and worst-case CVaR (wcCVaR) constraints in diffusion model and the risk measure limit is proportional to company’s surplus in hand. In the dynamic setting, a CVaR/wcCVaR constraint is equivalent to a VaR constraint under a higher confidence level. Applying dynamic programming technique, we obtain closed form expressions of the optimal reinsurance strategies and corresponding survival probabilities under both proportional and excess-of-loss reinsurance. Several numerical examples are provided to illustrate the impact caused by dynamic VaR/CVaR/wcCVaR limit in both types of reinsurance policy.
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