有交易费的未定权益无套利定价区间

本文首先给出了有交易费资产模型下套利机会的定义,利用辅助鞅和资产折算函数等方法,讨论了该模型下未定权益无套利定价问题,得到的结果是有交易费的未定权益无套利定价区间.     

有交易的未定权益无套利定价区间

本文首先给出了有效交易费资产模型下套利机会的定义，利用辅助鞅和资产折算函数等方法，讨论了该模型下未定权益无套利定价问题，得到的结果是有效易费的未定权益无套利定价区间。     

外汇期权的多维跳-扩散模型

本文建立了外汇期权的多维跳-扩散模型,在此模型下将外汇欧式未定权益的定价问题归结为一类倒向随机微分方程的求解问题,证明了这类倒向随机微分方程适应解的存在唯一性问题,并给出了一个关于外汇欧式未定权益的定价公式.     

具有两类交易费的欧式未定权益定价

本考虑了在具有成比例和固定两类交易费情形下欧式未定权量的定价问题．通过引入脉冲随机控制，定义欧式未定权益的销售价，利用渐近分析的方法，得到其销售价为理想市场的欧式未定价格摄动。     

基于连续红利支付和随机波动率的未定权益定价模型

研究了具有连续红利支付和随机波动率的未定权益定价问题,利用等价鞅测度的方法推导了风险中性下的欧式未定权益定价公式．     

最小方差准则下一个未定权益的近似对冲

本文研究了不完备的离散时间股票市场下未定权益的定价的对冲问题.利用在最小方差准则下选择概率测度Q或权重函数LN来求最优投资组合的方法,给出了离散时间情况下的鞅表示定理,在最小方差准则下提供一个简单的方法来近似对冲一个未定权益或一个欧氏期权.     

定价问题和一类倒向随机微分方程解的存在唯一性

本文建立了由一个多维Brown运动、Poisson过程和跳时固定的简单点过程共同驱动的股票价格模型．在此模型下，将未定权益的定价问题归结为一类倒向随机微分方程的求解问题．证明了这类倒向随机微分方程适应解的存在唯一性问题，并给出了一个关于未定权益的定价公式．     

随机支付型未定权益的风险最小套期保值

讨论了具有随机支付型未定权益的风险最小套期问题.假定市场中存在两类具有不同市场信息的投资者,对于一个预先给定的随机支付流未定权益,利用Galtchouk-Kunita-Watanabe分解和L2空间投影定理证明了风险最小策略的存在性和唯一性,并给出了风险最小策略的构造方法.     

不完备证券市场中博弈未定权益的保值

考虑不完备证券市场中博弈未定权益(GCC)的保值问题,通过Kramkov关于上鞅的可选分解定理给出未定权益的上保值价格和下保值价格。指出关于买卖双方都存在着一个最优保值策略。给出价格的一个无套利区间,并针对前面的结论,给出几个性质以及在限制投资组合方面的一个应用。     

随机利率情形下跳-扩散模型的未定权益定价

讨论Vasicek短期利率模型下,风险资产的价格过程服从跳-扩散过程的欧式未定权益定价问题,利用鞅方法得到了欧式看涨期权和看跌期权定价公式及平价关系,最后给出了基于风险资产支付连续红利收益的欧式期权定价公式.     

Worst portfolios for dynamic monetary utility processes

We study the worst portfolios for a class of law invariant dynamic monetary utility functions with domain in a class of stochastic processes. The concept of comonotonicity is introduced for these processes in order to prove the existence of worst portfolios. Using robust representations of monetary utility function processes in discrete time, a relation between the worst portfolios at different periods of time is presented. Finally, we study conditions to achieve the maximum in the representation theorems for concave monetary utility functions that are continuous for bounded decreasing sequences.     

On optimal allocation of risk vectors

In this paper we extend results on optimal risk allocations for portfolios of real risks w.r.t. convex risk functionals to portfolios of risk vectors. In particular we characterize optimal allocations minimizing the total risk as well as Pareto optimal allocations. Optimal risk allocations are shown to exhibit a worst case dependence structure w.r.t. some specific max-correlation risk measure and they are comonotone w.r.t. a common worst case scenario measure. We also derive a new existence criterion for optimal risk allocations and discuss some examples.     

Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes ‘weights’ of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.     

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.     

On value preserving and growth optimal portfolios

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with the minimal martingale measure only for complete markets.     

Stochastic Nonstationary Optimization for Finding Universal Portfolios

We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that class of portfolios which are constructed directly from the available observations of the stocks behavior without any assumptions about their statistical properties. Cover [7] has shown that one can construct such portfolio using only observations of the past stock prices which generates the same asymptotic wealth growth as the best constant rebalanced portfolio which is constructed with the full knowledge of the future stock market behavior.In this paper we construct universal portfolios using a different set of ideas drawn from nonstationary stochastic optimization. Our portfolios yield the same asymptotic growth of wealth as the best constant rebalanced portfolio constructed with the perfect knowledge of the future and they are less demanding computationally compared to previously known universal portfolios. We also present computational evidence using New York Stock Exchange data which shows, among other things, superior performance of portfolios which explicitly take into account possible nonstationary market behavior.     

Robust static hedging of barrier options in stochastic volatility models

Static hedge portfolios for barrier options are extremely sensitive with respect to changes of the volatility surface. In this paper we develop a semi-infinite programming formulation of the static super-replication problem in stochastic volatility models which allows to robustify the hedge against model parameter uncertainty in the sense of a worst case design. From a financial point of view this robustness guarantees the hedge performance for an infinite number of future volatility surface scenarios including volatility shocks and changes of the skew. After proving existence of such robust hedge portfolios and presenting an algorithm to numerically solve the underlying optimization problem, we apply the approach to a detailed example. Surprisingly, the optimal robust portfolios are only marginally more expensive than the barrier option itself.     

A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation

We present a new approach to asset allocation with transaction costs. A multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio. Received: August 15, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Peng et al (Int J Uncertain Fuzziness Knowl Based Syst 15:29–41, 2007) introduced, by means of the credibility measure, two dominance relations on fuzzy variables, namely the first- and the second-order dominances. In this paper, we characterize each of these dominance relations, and we justify that they satisfy six well-known properties of comparison methods. We propose a Game Theory approach for the determination of optimal portfolios when returns are fuzzy by introducing the set of best portfolios with respect to the first- and the second-order dominances. Based on the characterization of the first-order dominance, we numerically display some of the best portfolios of the classical set of portfolios of seven independent assets described by triangular fuzzy numbers.