带机会约束的动态投资决策模型研究

Research on a Dynamic Investment Decision Model with Constraint of Investment Chance

本文在Black Scholes型市场中 ,建立了具有投资机会约束的CaR动态投资决策模型 :minx∈RdCaR(x ,π ,T) s t Prob(Xπ(T)≥R)≥β ,其中x是初始财富 ,π(t) =(π1(t) ,… ,πd(t) )′∈Rd 为可行的证券组合过程 ,Xπ(T)为计划期末的财富水平 ,CaR(x ,π ,T)为投资期末的在险资本 ,R是投资者事先给定的某正的财富水平 ,0 <β <1 通过对该模型的讨论 ,得到了最优常数再调整策略的显式表达式 ,其金融学含义包括 :对于机会约束下的动态投资组合 ,在风险中性市场中 ,最优的常数再调整投资策略是纯债券投资策略 ,最优的在险资本值为零 ;在风险非中性市场中 。

In Black-Scholes type financial markets,the CaR dynamic portfolio decision model with constraint of investment chance is established as following: minx∈R^dCaR(x,π,T) s.t.Prob(X~π(T)≥R)≥β, where x is the initial wealth,π(t)=(π_1(t),...,π_d(t))′∈R^d is the process of feasible portfolio,X~π(T)is the terminal wealth,R is a positive wealth level given by investor and 0<β<1.The explicit solutions for this model are obtained in terms of the optimal constant rebalance strategy.The financial interpretations of the results include that,for portfolio decision with constraint of investment chance,the optimal constant rebalance strategy is pure bond investment strategy and the optimal Capital-at-Risk is zero in neutral risk markets,and the optimal constant rebalance strategy implies the mutual fund theorem in non-neutral risk markets.