Lyapunov-type inequalities for certain higher order differential equations with anti-periodic boundary conditions

In this work, we will establish several new Lyapunov-type inequalities for certain half-linear higher order differential equations with anti-periodic boundary conditions. A lower bound of eigenvalues will be also given.     

基于ICA-SV模型的金融市场协同波动溢出分析及实证研究

对于动态投资组合与风险管理来说,测定波动溢出效应是非常重要的.已有的文献证明SV模型比GARCH模型能够更好地刻画金融市场的波动,使用SV模型研究两个金融市场间波动溢出的文献并不多见,而使用SV模型研究多个金融市场对一个金融市场协同波动溢出的文献则更为少见.本文以独立成分表示金融市场波动的协同指标,提出了独立成分SV模型(ICA-SV),并研究了多个金融市场对一个金融市场的协同波动溢出,实证结果验证了ICA-SV模型在分析金融市场协同波动溢出是可行的.     

Investment–consumption with regime-switching discount rates

This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switch according to a finite state Markov chain. The change in the discount rate leads to time inconsistencies of the investor’s decisions. The randomness in our model is driven by a Brownian motion and a Markov chain. Following Ekeland and Pirvu (2008) we introduce and characterize the subgame perfect strategies. Numerical experiments show the effect of time preference on subgame perfect strategies and the pre-commitment strategies.     

Combining chain-ladder claims reserving with fuzzy numbers

In this paper we extend the classical chain-ladder claims reserving method using fuzzy methods. Therefore, we derive new estimators for the claims development factors as well as new predictors for the ultimate claims. The advantage in using fuzzy numbers lies in the fact that the model uncertainty is directly included in and can be controlled by the “new” fuzzy claims development factors. We also provide an estimator for the uncertainty of the ultimate claims for single accident years and for aggregated accident years.     

On geometric ergodicity of skewed—SVCHARME models

Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by the hidden Markov Chain with switching.     

Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework

This paper investigates an optimal investment strategy of DC pension plan in a stochastic interest rate and stochastic volatility framework. We apply an affine model including the Cox–Ingersoll–Ross (CIR) model and the Vasicek mode to characterize the interest rate while the stock price is given by the Heston’s stochastic volatility (SV) model. The pension manager can invest in cash, bond and stock in the financial market. Thus, the wealth of the pension fund is influenced by the financial risks in the market and the stochastic contribution from the fund participant. The goal of the fund manager is, coping with the contribution rate, to maximize the expectation of the constant relative risk aversion (CRRA) utility of the terminal value of the pension fund over a guarantee which serves as an annuity after retirement. We first transform the problem into a single investment problem, then derive an explicit solution via the stochastic programming method. Finally, the numerical analysis is given to show the impact of financial parameters on the optimal strategies.     

Optimal dividend and investing control of an insurance company with higher solvency constraints

This paper considers the optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. This paper aims at describing the optimal return function as well as the optimal policy. As a by-product, the paper theoretically sets a risk-based capital standard to ensure the capital requirement that can cover the total risk.     

Lot-sizing two-echelon assembly systems with random yields and rigid demand

We consider a two-echelon assembly system producing a single final product for which the demand is known. The first echelon consists of several parallel stages, whereas the second echelon consists of a single assembly stage. We assume that the yield at each stage is random and that demand needs to be satisfied in its entirety; thus, several production runs may be required. A production policy should specify, for each possible configuration of intermediate inventories, on which stage to produce next and the lot size to be processed. The objective is to minimize the expected total of setup and variable production costs.We prove that the expected cost of any production policy can be calculated by solving a finite set of linear equations whose solution is unique. The result is general in that it applies to any yield distribution. We also develop efficient algorithms leading to heuristic solutions with high precision and, as an example, provide numerical results for binomial yields.