TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS

We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner’s theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure‐valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction‐triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.     

OPTIMAL LIQUIDATION OF DERIVATIVE PORTFOLIOS

We consider the problem facing a risk averse agent who seeks to liquidate or exercise a portfolio of (infinitely divisible) perpetual American style options on a single underlying asset. The optimal liquidation strategy is of threshold form and can be characterized explicitly as the solution of a calculus of variations problem. Apart from a possible initial exercise of a tranche of options, the optimal behavior involves liquidating the portfolio in infinitesimal amounts, but at times which are singular with respect to calendar time. We consider a number of illustrative examples involving CRRA and CARA utility, stocks, and portfolios of options with different strikes, and a model where the act of exercising has an impact on the underlying asset price.     

ASSET ALLOCATION AND ANNUITY-PURCHASE STRATEGIES TO MINIMIZE THE PROBABILITY OF FINANCIAL RUIN

In this paper, we derive the optimal investment and annuitization strategies for a retiree whose objective is to minimize the probability of lifetime ruin, namely the probability that a fixed consumption strategy will lead to zero wealth while the individual is still alive. Recent papers in the insurance economics literature have examined utility-maximizing annuitization strategies. Others in the probability, finance, and risk management literature have derived shortfall-minimizing investment and hedging strategies given a limited amount of initial capital. This paper brings the two strands of research together. Our model pre-supposes a retiree who does not currently have sufficient wealth to purchase a life annuity that will yield her exogenously desired fixed consumption level. She seeks the asset allocation and annuitization strategy that will minimize the probability of lifetime ruin. We demonstrate that because of the binary nature of the investor's goal, she will not annuitize any of her wealth until she can fully cover her desired consumption with a life annuity. We derive a variational inequality that governs the ruin probability and the optimal strategies, and we demonstrate that the problem can be recast as a related optimal stopping problem which yields a free-boundary problem that is more tractable. We numerically calculate the ruin probability and optimal strategies and examine how they change as we vary the mortality assumption and parameters of the financial model. Moreover, for the special case of exponential future lifetime, we solve the (dual) problem explicitly. As a byproduct of our calculations, we are able to quantify the reduction in lifetime ruin probability that comes from being able to manage the investment portfolio dynamically and purchase annuities.     

PORTFOLIO SELECTION PROBLEMS VIA THE BIVARIATE CHARACTERIZATION OF STOCHASTIC DOMINANCE RELATIONS1

Stochastic dominance (SD) is a very useful tool in various areas of economics and finance. the purpose of this paper is to provide the results of SD relations developed in other areas such as applied probability which, we believe, are useful for many portfolio selection problems. In particular, the bivariate characterization of SD relations given by Shanthikumar and Yao (1991) is a powerful tool for the demand and the shift effect problems in optimal portfolios. the method enables one to extend many results that hold for the case where the underlying lying assets are statistically independent to the dependent case directly.     

中国生猪价格周期性波动分析、展望及对策

2006年以来,中国生猪价格波动经历了三个半周期,呈现出价格波动周期日益延长、价格波动幅度前窄后宽、传统消费旺季作用逐渐消退等特征。其中既有生猪养殖自身规律、规模化养殖比例提升等内因的影响,也有上游行业价格变动、生猪疫情等外因的影响。综合来看,2019年非洲猪瘟疫情发展、规模化生猪养殖场补栏、气温条件变化及冬季的猪肉旺季消费等情况会对后续的生猪价格波动走势产生较大影响,至2020年春节前生猪价格持续走高。应通过加快生猪养殖产业结构升级、加强生猪市场信息服务体系建设、推进生猪产业链市场化发展等措施,有效减缓中国生猪价格周期波动的影响。     

PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESS

We consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov-modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor's aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized Hamilton–Jacobi–Bellman equation where we replace the derivative by Clarke's generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular, we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy.