Valuing risky income streams in incomplete markets

A model for pricing and hedging in incomplete markets is proposed. This model is derived from expected utility theory, and a connection with the traditional no‐arbitrage framework is noted. It is shown that the CGM model can be implemented to value risky assets in incomplete markets.     

Option pricing in incomplete markets

Expected utility maximization is a very useful approach for pricing options in an incomplete market. The results from this approach contain many important features observed by practitioners. However, under this approach, the option prices are determined by a set of coupled nonlinear partial differential equations in high dimensions. Thus, it represents numerous significant difficulties in both theoretical analysis and numerical computations. In this paper, we present accurate approximate solutions for this set of equations.     

Sensitivity of optimal consumption streams

We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. At the leading order, the consumption adjustment does not matter: any choice that matches the budget constraint simply shifts the original utility by the marginal value of the perturbation. Nontrivial results can be obtained by considering the next-to-leading order. Here, one first solves the problem for a deterministic perturbation, which leads to a “prognosis measure”. The desired consumption adjustment for a general endowment perturbation is in turn given by the conditional expectation of the latter, computed under this measure and appropriately weighted with the conditional expectations of the remaining risk-tolerance.     

Evaluation of insurance products with guarantee in incomplete markets

Life insurance products are usually equipped with minimum guarantee and bonus provision options. The pricing of such claims is of vital importance for the insurance industry. Risk management, strategic asset allocation, and product design depend on the correct evaluation of the written options. Also regulators are interested in such issues since they have to be aware of the possible scenarios that the overall industry will face. Pricing techniques based on the Black & Scholes paradigm are often used, however, the hypotheses underneath this model are rarely met.To overcome Black & Scholes limitations, we develop a stochastic programming model to determine the fair price of the minimum guarantee and bonus provision options. We show that such a model covers the most relevant sources of incompleteness accounted in the financial and insurance literature. We provide extensive empirical analyses to highlight the effect of incompleteness on the fair value of the option, and show how the whole framework can be used as a valuable normative tool for insurance companies and regulators.     

Optimal consumption and arbitrage in incomplete,finite state security markets

We study a consistent treatment for both the multi-period portfolio selection problem and the option attainability problem by a dual approach. We assume that time is discrete, the horizon is finite, the sample space is finite and the number of securities is less than that of the possible securities price transitions, i.e. an incomplete security market. The investor is prohibited from investing stocks more than given linear investment amount constraints at any time and he maximizes an expected additive utility function for the consumption process. First we give a set of budget feasibility conditions so that a consumption process is attainable by an admissible portfolio process. To establish this relation, we used an algorithmic approach which has a close connection with the linear programming duality. Then we prove the unique existence of a primal optimal solution from the budget feasibility conditions. Finally, we formulate a dual control problem and establish the duality between primal and dual control problems.We are grateful to the editor, Hiroshi Konno, and two anonymous referees for their valuable comments and constructive suggestions on this research. We are responsible for the remaining errors. The first author is supported in part by the fund endowed to the Research Association for Financial Engineering by Toyo Trust Bank Co. and Mito Shoken Co.     

我国农民消费问题的分省面板协整模型分析

依据现代消费理论,在符合中国经济现实假设条件下,建立了我国农民消费问题的数理函数。使用1980-2006年的宏观消费数据,通过协整模型分析表明我国农民的边际消费倾向约为0.69;基于Hausman检验的固定效应模型的面板单位根和面板协整对我国30个省份分析结果表明边际消费倾向为0.7;变截距变斜率面板模型表明各省的长期自主消费和长期边际消费倾向差异显著,上海、江苏呈现双高特征,吉林、海南和西藏则呈现双低特征,其他省份则表现为自主消费和边际消费倾向两者此高彼低的特点。差异产生的原因在于消费习惯不同以及收入差异导致的"主动、被动"消费造成的结果,提出了为西部增收以促进消费良性循环的合理的政策建议。     

Geometry of polar wedges in Riesz spaces and super-replication prices in incomplete financial markets

This paper is devoted to a further generalisation of the main results in [5] including the representation of the weak super-replication price (cf. equation (1.6)). In addition to the already established weakening of the technical assumptions in [5] (cf. [24] and [25]), the main results in [5] can be still generalised by considering the geometric structure of the underlying problem (based on the properties of Riesz spaces and polar wedges therein). In Section 5 we show under which geometric conditions of the relevant sets the results still hold (cf. Theorem 5.3 and Corollary 5.5). In particular, we can completely remove the restrictive admissibility assumption and carry forward equation (1.4) to a larger class of wedges (cf. Corollary 5.5). The authors gratefully acknowledge support from EPSRC grant no. GR/S80202/01     

The path player game

We give an explicit PDE characterization for the solution of the problemof maximizing the utility of both terminal wealth and intertemporal consumption undermodel uncertainty. The underlying market model consists of a risky asset, whosevolatility and long-term trend are driven by an external stochastic factor process. Therobust utility functional is defined in terms of a HARA utility function with risk aversionparameter 0 < α < 1 and a dynamically consistent coherent risk measure, whichallows for model uncertainty in the distributions of both the asset price dynamics andthe factor process. Ourmethod combines recent results by Wittmüß (Robust optimizationof consumption with random endowment, 2006) on the duality theory of robustoptimization of consumption with a stochastic control approach to the dual problemof determining a ‘worst-case martingale measure’.     

A DIRECT METHOD IN OPTIMAL PORTFOLIO AND CONSUMPTION CHOICE

In this paper, we use a direct method to solve the optimal portfolio and consumption choice problem in the security market for a specific case, in which the utility function is of a given homogenous form, i.e. the so-called CRRA case. The idea comes from the completion technique ever used in LQ optimal control.     

On optimal partial hedging in discrete markets

The paper considers arbitrage-free discrete markets representing them in the form of scenario trees. Two well-known problems of quantile hedging and hedging with minimal risk of shortfall are analysed. Methods of solving these problems are discussed. The dynamic programming algorithm is used to build the hedging strategy.     

我国居民消费倾向的实证分析

依据国家统计局颁布的“中国统计年鉴 ( 99年 )”资料 ,通过研究消费、收入与储蓄的关系 ,证实了我国居民在经济转轨期内的消费倾向 ,并对居民的八项消费性支出进行了统计聚类分析和因子分析 ,获得了我国城乡居民消费性支出的地区谱系和消费共性。     

HARA frontiers of optimal portfolios in stochastic markets

In this paper, we consider the optimal portfolio selection problem in continuous-time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has the structure of the HARA family and the market states change according to a Markov process. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. We analyzed Black–Scholes type continuous-time models where the market parameters are driven by Markov processes. The Markov process that affects the state of the market is independent of the underlying Brownian motion that drives the stock prices. The problem of maximizing the expected utility of the terminal wealth is investigated and solved by stochastic optimal control methods for exponential, logarithmic and power utility functions. We found explicit solutions for optimal policy and the associated value functions. We also constructed the optimal wealth process explicitly and discussed some of its properties. In particular, it is shown that the optimal policy provides linear frontiers.     

Price bounds of mortality-linked security in incomplete insurance market

This study investigates reasonable price bounds for mortality-linked securities when the issuer has only a partial hedging ability. The price bounds are established by minimizing the difference between the benchmark price and the replicating portfolio cost subject to the gain–loss ratio of excess payoff of the mortality-linked securities. In contrast to the previous studies, the assumptions of no-arbitrage pricing and utility-based pricing are not fully employed in this study because of the incompleteness of the insurance securitization market. Instead, a framework including three insurance basis assets is constructed to search for the price bounds of mortality-linked securities and use the Swiss Re mortality catastrophe bond, issued in 2003, as a numerical example. The proposed price bounds are valuable for setting bid–asked spreads and coupon premiums, and establishing trading strategies in the raising mortality securitization markets.     

随机市场中均值-方差模型最优投资策略的时间不相容性及其修正

由于方差算子在动态规划意义下不可分,导致随机市场中多期均值一方差模型的最优投资策略不满足时间相容性,即Bellman最优性原理．为此,首先提出了随机市场中比Bellman最优性原理更弱的时间相容性,并证明在投资区间的任意中间时刻,当投资者的财富不超过某一给定的财富阈值时,最优投资策略满足弱时间相容性;当投资者的财富超过该阈值时,最优投资策略将不再是弱时间相容的,且导致投资者变为非理性,即他会同时极小化终期财富的均值和方差．在这种情形下,通过放松自融资约束,对最优投资策略进行了修正,使得其满足：修正策略可使投资者回归理性;相对于终期财富,修正策略可以获得与最优投资策略相同的均值和方差．在策略修正过程中,投资者可以从市场中获得一个严格正的现金流．这些结果表明修正策略要优于原最优投资策略,拓展了现有关于确定市场下多期均值．方差模型的求解以及策略时间相容性的结论．     

Risk management in power markets: The Hedging value of production flexibility

Since the 1990s power markets are being restructured worldwide and nowadays electrical power is traded as a commodity. The liberalization and with it the uncertainty in gas, fuel and electrical power prices requires an effective management of production facilities and financial contracts. Thereby derivatives build essential instruments to exchange volume as well as price risks. The challenge for participants in the newly competitive market environment is how to design, price and hedge derivative contracts in particular combination with the flexibility embedded in dispatch strategies of production assets. Accordingly, an adequate basis for management and investment decisions is needed which responds to the highly complex market situation.     

The computing of the optimal power consumption for semi-track air-cushion vehicle using hybrid generalized extremal optimization

A new stochastic method named hybrid generalized extremal optimization (HGEO) is proposed in this paper. It combines genetic algorithms (GAs) and generalized extremal optimization (GEO). In order to extend GEO’s mutation operator to accelerate convergence speed and be easily incorporated into HGEO, the real coded GEO is first developed to population-base GEO (PGEO), and then incorporated into the HGEO in the paper. Constraints consideration for using the HGEO and the effects of related operators are also investigated. Finally, the performance of the HGEO is fully investigated compared with other related algorithms to find the optimal power consumption for the semi-track air-cushion vehicle (STACV). The results show that the HGEO has better performance than GAs or other related simpler algorithms.     

The game for the speed of convergence in repeated games of incomplete information

We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer is the (more) informed player. Such games have value v _∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to v _∞ (p) (and will converge from above to v _∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence of the average payoffs-to the value v _∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG _∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v _n (p)− v _∞ (p) is of the order of magnitude of . In that case the value of SG _∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛^∞={X _k }^∞ _k=1, one defines for each n : V _n (𝔛^∞) ≔E∑ⁿ _k=1 |X _k+1 − X _k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛^∞, V _n (𝔛^∞) can be of the order of magnitude of n ^1/2−ε, for arbitrarily small ε>0. Received January 1999/Final version April 2002     

The fundamental theorem of asset pricing under default and collateral in finite discrete time

We consider a financial market where time and uncertainty are modeled by a finite event-tree. The event-tree has a length of N, a unique initial node at the initial date, and a continuum of branches at each node of the tree. Prices and returns of J assets are modeled, respectively, by a R2J×R2J-valued stochastic process . In this framework we prove a version of the Fundamental Theorem of Asset Pricing which applies to defaultable securities backed by exogenous collateral suffering a contingent linear depreciation.     

多元统计在山东农村居民消费结构分析中的应用

本运用多元统计的因子分析、聚类分析法，对山东各地区农村居民的消费结构进行统计分析；然后在将山东省农村各地区分为四类的基础上，分析比较各类地区消费结构的差异及其成因；最后就如何促进山东农村居民合理消费，以此拉动山东农村经济的发展，提出相应的建议．