Utility maximization in markets with bid–ask spreads

A one-period financial market model with transaction costs is considered in this paper. Redefining the risky asset price process in a suitable way, we obtain an explicit solution to the utility maximization problem when the risk preferences of the investor are based on the exponential utility function and a liability can be included in her portfolio. The arbitrage-free interval price for a general liability, as well as its replication price, is characterized in terms of expectations with respect to equivalent martingale measures. The indifference price is derived and its asymptotic limit when the risk aversion is going to infinity is analysed.     

A scenario aggregation algorithm for the solution of stochastic dynamic minimax problems

In this paper, we present a scenario aggregation algorithm for the solution of the dynamic minimax problem in stochastic programming. We consider the case where the joint probability distribution has a known finite support. The algorithm applies the Alternating Direction of Multipliers Method on a reformulation of the minimax problem using a double duality framework. The problem is solved by decomposition into scenario sub-problems, which are deterministic multi-period problems. Convergence properties are deduced from the Alternating Direction of Multipliers. The resulting algorithm can be seen as an extension of Rockafellar and Wets Progressive Hedging algorithm to the dynamic minimax context.     

探析两个法律语类中的模糊限制语的社会-认知方面

从社会认知的角度分析美国最高法院意见书和美国法律评论文章中的模糊限制语。两个语类之间的差异可与语类本身的某些特征尤其是语境和交际目的相联系,因而,就法律语类而言,模糊限制语是因语类而异的。     

Asymptotic pricing in large financial markets

The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the α-quantile price is shown. The large Black–Scholes model is carefully examined.      

Discrete–time delta hedging and the Black–Scholes model with transaction costs

The paper deals with the problem of discrete–time delta hedging and discrete-time option valuation by the Black–Scholes model. Since in the Black–Scholes model the hedging is continuous, hedging errors appear when applied to discrete trading. The hedging error is considered and a discrete-time adjusted Black–Scholes–Merton equation is derived. By anticipating the time sensitivity of delta in many cases the discrete-time delta hedging can be improved and more accurate delta values dependent on the length of the rebalancing intervals can be obtained. As an application the discrete-time trading with transaction costs is considered. Explicit solution of the option valuation problem is given and a closed form delta value for a European call option with transaction costs is obtained.     

Efficient hedging with coherent risk measure

The idea of efficient hedging has been introduced by Föllmer and Leukert. They defined the shortfall risk as the expectation of the shortfall weighted by a loss function, and looked for strategies that minimize the shortfall risk under a capital constraint. In this paper, to measure the shortfall risk, we use the coherent risk measures introduced by Artzner, Delbaen, Eber and Heath. We show that, for a given contingent claim H, the optimal strategy consists in hedging a modified claim ?H for some randomized test ?. This is an analogue of the results by Föllmer and Leukert.     

Supply chain network equilibrium with strategic financial hedging using futures

In this paper, we develop a network equilibrium model for supply chain networks with strategic financial hedging. We consider multiple competing firms that purchase multiple materials and parts to manufacture their products. The supply chain firms’ procurement activities are exposed to commodity price risk and exchange rate risk. The firms can use futures contracts to hedge the risks. Our research studies the equilibrium of the entire network where each firm optimizes its own operation and hedging decisions. We use variational inequality theory to formulate the equilibrium model, and provide qualitative properties. We provide analytical results for a special case with duopolistic competition, and use simulations to study an oligopolistic case. The analytical and simulation studies reveals interesting managerial insights.     

Mean‐variance hedging with basis risk

Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuities, etc. In the presence of basis risk, a perfect hedging is impossible, and in this paper, we adopt a mean‐variance criterion to strike a balance between the expected hedging error and its variability. Under a time‐dependent diffusion model setup, explicit optimal solutions are derived for the hedging target being either a European option or a forward contract. The solutions are obtained by a delicate application of the linear quadratic control theory, the method of backward stochastic differential equation, and Malliavin calculus. A numerical example is presented to illustrate our theoretical results and their interesting implications.     

进行期货套期保值的最优组合问题

讨论了为规避由于资产价格波动将来可能面临的风险、选择期货和期货组合进行套期保值的问题.通过建立相应的数学模型,给出了最优解,得到了极具实际操作意义的结果.     

Convergence and optimality of BS-type discrete hedging strategy under stochastic interest rate

We focus on the asymptotic convergence behavior of the hedging errors of European stock option due to discrete hedging under stochastic interest rates. There are two kinds of BS-type discrete hedging differ in hedging instruments: one is the portfolio of underlying stock, zero coupon bond, and the money market account (Strategy BSI); the other is the underlying stock, zero coupon bond (Strategy BSII). Similar to the results of the deterministic interest rate case, we show that convergence speed of the disco...