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.     

EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE MEAN-VARIANCE CAPITAL MARKET

We derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balances in the standard mean-variance capital market. Also, we give an explicit formula for such a price vector. This formula shows that the price of assets is an increasing function of , the weighted average of the requested rate of return of individual investors, which tends to infinity as approaches the expected rate of return on the market portfolio. Further, we construct a macroeconomic index which gives information about the soundness of the capital market.     

THE EFFECT OF ESTIMATION IN HIGH‐DIMENSIONAL PORTFOLIOS

We study the effect of estimated model parameters in investment strategies on expected log‐utility of terminal wealth. The market consists of a riskless bond and a potentially vast number of risky stocks modeled as geometric Brownian motions. The well‐known optimal Merton strategy depends on unknown parameters and thus cannot be used in practice. We consider the expected utility of several estimated strategies when the number of risky assets gets large. We suggest strategies which are less affected by estimation errors and demonstrate their performance in a real data example. Strategies in which the investment proportions satisfy an L₁ ‐constraint are less affected by estimation effects.     

PORTFOLIOS OF AMERICAN OPTIONS UNDER GENERAL PREFERENCES: RESULTS AND COUNTEREXAMPLES

We consider the optimal exercise of a portfolio of American call options in an incomplete market. Options are written on a single underlying asset but may have different characteristics of strikes, maturities, and vesting dates. Our motivation is to model the decision faced by an employee who is granted options periodically on the stock of her company, and who is not permitted to trade this stock. The first part of our study considers the optimal exercise of single options. We prove results under minimal assumptions and give several counterexamples where these assumptions fail—describing the shape and nesting properties of the exercise regions. The second part of the study considers portfolios of options with differing characteristics. The main result is that options with comonotonic strike, maturity, and vesting date should be exercised in order of increasing strike. It is true under weak assumptions on preferences and requires no assumptions on prices. Potentially the exercise ordering result can significantly reduce the complexity of computations in a particular example. This is illustrated by solving the resulting dynamic programming problem in a constant absolute risk aversion utility indifference model.     

NEWS-GENERATED DEPENDENCE AND OPTIMAL PORTFOLIOS FOR n STOCKS IN A MARKET OF BARNDORFF-NIELSEN AND SHEPHARD TYPE

We consider Merton's portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein–Uhlenbeck type. The investor can trade in n stocks and a risk-free bond. We assume that the dependence between stocks lies in that they partly share the Ornstein–Uhlenbeck processes of the volatility. We refer to these as news processes, and interpret this as that dependence between stocks lies solely in their reactions to the same news. The model is primarily intended for assets that are dependent, but not too dependent, such as stocks from different branches of industry. We show that this dependence generates covariance, and give statistical methods for both the fitting and verification of the model to data. Using dynamic programming, we derive and verify explicit trading strategies and Feynman–Kac representations of the value function for power utility.     

THE EXPECTED SHORTFALL OF QUADRATIC PORTFOLIOS WITH HEAVY‐TAILED RISK FACTORS

Computable expressions are derived for the Expected Shortfall of portfolios whose value is a quadratic function of a number of risk factors, as arise from a Delta–Gamma–Theta approximation. The risk factors are assumed to follow an elliptical multivariate t distribution, reflecting the heavy‐tailed nature of asset returns. Both an exact expression and a uniform asymptotic expansion are presented. The former involves only a single rapidly convergent integral. The latter is essentially explicit, and numerical experiments suggest that its error is negligible compared to that incurred by the Delta–Gamma–Theta approximation.     

EFFICIENT HEDGING OF EUROPEAN OPTIONS WITH ROBUST CONVEX LOSS FUNCTIONALS: A DUAL‐REPRESENTATION FORMULA

Motivated by numerical representations of robust utility functionals, due to Maccheroni et al., we study the problem of partially hedging a European option H when a hedging strategy is selected through a robust convex loss functional L(·) involving a penalization term γ(·) and a class of absolutely continuous probability measures . We present three results. An optimization problem is defined in a space of stochastic integrals with value function EH(·) . Extending the method of Föllmer and Leukerte, it is shown how to construct an optimal strategy. The optimization problem EH(·) as criterion to select a hedge, is of a “minimax” type. In the second, and main result of this paper, a dual‐representation formula for this value is presented, which is of a “maxmax” type. This leads us to a dual optimization problem. In the third result of this paper, we apply some key arguments in the robust convex‐duality theory developed by Schied to construct optimal solutions to the dual problem, if the loss functional L(·) has an associated convex risk measure ρ^L(·) which is continuous from below, and if the European option H is essentially bounded.     

OVERLAPPING SETS OF PRIORS AND THE EXISTENCE OF EFFICIENT ALLOCATIONS AND EQUILIBRIA FOR RISK MEASURES

The overlapping expectations and the collective absence of arbitrage conditions introduced in the economic literature to insure existence of Pareto optima and equilibria with short‐selling when investors have a single belief about future returns, is reconsidered. Investors use measures of risk. The overlapping sets of priors and the Pareto equilibrium conditions introduced by Heath and Ku for coherent risk measures are respectively reinterpreted as a weak no‐arbitrage and a weak collective absence of arbitrage conditions and shown to imply existence of Pareto optima and Arrow–Debreu equilibria.     

零售业如何建立高效的物流体系

企业的高速运行有赖于一流的物流管理体系 ,这是快速变革的时代对企业的要求 ,也是企业生死存亡的战略依托。要建立高效的物流 ,就要解决几个最根本的问题并采取相应的物流战略策略。     

HEDGING STRATEGIES AND MINIMAL VARIANCE PORTFOLIOS FOR EUROPEAN AND EXOTIC OPTIONS IN A LÉVY MARKET

This paper presents hedging strategies for European and exotic options in a Lévy market. By applying Taylor’s theorem, dynamic hedging portfolios are constructed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk‐free bank account, the underlying asset, and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.     

EFFICIENT PRICING OF BARRIER OPTIONS AND CREDIT DEFAULT SWAPS IN LÉVY MODELS WITH STOCHASTIC INTEREST RATE

Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of Lévy models, the Heston model, and other affine models. Similar deformations were used in one‐factor Lévy models to price options with barrier and lookback features and credit default swaps (CDSs). In the present paper, we generalize this approach to models, where the dynamics of the assets is modeled as , where X is a Lévy process, and the interest rate is stochastic. Assuming that X and r are independent, and , the infinitesimal generator of the pricing semigroup in the model for the short rate, satisfies weak regularity conditions, which hold for popular models of the short rate, we develop a variation of the pricing procedure for Lévy models which is almost as fast as in the case of the constant interest rate. Numerical examples show that about 0.15 second suffices to calculate prices of 8 options of same maturity in a two‐factor model with the error tolerance and less; in a three‐factor model, accuracy of order 0.001–0.005 is achieved in about 0.2 second. Similar results are obtained for quanto CDS, where an additional stochastic factor is the exchange rate. We suggest a class of Lévy models with the stochastic interest rate driven by 1–3 factors, which allows for fast calculations. This class can satisfy the current regulatory requirements for banks mandating sufficiently sophisticated credit risk models.     

沉浮新大陆

天上掉馅饼的好事不是没有，但大多早已付出代价。每当经济危机退潮之时，总有新技术横空出世，物联网概念也借此一飞冲天，一家叫新大陆的企业因此浮出水面成为公众焦点，其实他们已经在寂寞中苦苦坚持了十年。     

皱纹撒谎的代价

我一直弄不懂,影视演员不是京剧演员——从事这"国粹"事业的人数这么少,由来已久的程式定得这么死:当老生非得演中年以上的,是花旦非得演年轻女子——年轻的影视演员多得如滚滚洪流,年轻的邓婕扮演年轻的王熙凤,蛮好,可后来为什么非要让四十几的刘晓庆演二十岁的王熙凤?累不累啊?去年,新版电视剧《红楼梦》纠正过来了,很年轻的姚笛演王熙凤。可是这小     

城市的细节

城市的细节无处不在,惟其如此,生活才变得越来越精彩。只是我们常常在不经意间疏忽了细节的存在,有的人因此便觉得生活的平常和乏味。实际上,许多人往往将自己的目光过多地集中在城市的高度,抑或自己的想象力上,于是,城市的细节也就成了过眼云烟,随风飘了去。这就应了"身在宝山不识     

“笼子”的价格

一个家好比一个“笼子”。“笼子”有华丽有简陋，有古典式有现代版，或占繁华闹市或居乡村僻野，里面的人则像是大大小小的鸟。一个人无论长得多大多高，在父母眼里总是小孩，就像一只小鸟，离不了“笼子”。     

一个总裁的梦——访ICONASIA公司总裁罗德文

8月初，正是上海最热的时候。推开罗德文的家门，他正在一个小本子上专注地记着什么，见我来了，才不舍地放下手中的笔。我好奇地想探个究竟，他说我要为梦想抓住稍纵既逝的念头。     

卡尔玛“卖点”

“中欧商贸展示中心”是中国迄今为止在瑞典投资的最大商业项目。孰料，“中心”甫一开业，引起热议不断：是中小企业集体“走出去”，还是变相从事移民中介？[编者按]     

酒香之旅

当越来越多的人喜爱上葡萄酒的时候,人们也对酒庄产生了浓厚兴趣。在产酒大国,如法国、西班牙、意大利、美国、澳大利亚等,都会有充满当地特色的葡萄酒之旅。所以酒庄也逐渐注重自己的形象,纷纷请来著名的设计师设计,希望人们品酒的同时,也对酒庄留下深刻印象。