We consider an agent who seeks to optimally invest and consume in the presence of proportional transaction costs. The agent can invest in two types of futures contracts, modeled as two correlated arithmetic Brownian motions, and in a money market account with constant rate of interest. She may also consume and get utility U(c) ≜cpp , c ≥ 0, where p ∈ (0, 1) and c is the rate of consumption. The agent can control the rate of consumption and influence the evolution of wealth by controlling the number of futures contracts held. Proportional transaction costs lambda i = alphailambda are charged for every trade in futures contracts of type i, i = 1, 2. All consumption is done from the money market account. The agent wishes to maximize the expected discounted integral over [0, infinity) of the utility of consumption. We compute an asymptotic expansion of the value function in powers of lambda1/3.
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机译:我们考虑一个在比例交易成本存在的情况下寻求最佳投资和消费的代理商。代理可以投资两种类型的期货合约(以两个相关的算术布朗运动为模型)以及具有恒定利率的货币市场账户。她还可以消费并获得效用U(c)≜ cpp,c≥0,其中p∈(0,1),c是消费率。代理人可以通过控制持有的期货合约的数量来控制消费率并影响财富的演变。比例交易成本lambda i = alphailambda是针对类型i,i = 1,2的期货合约的每笔交易收取的。所有消费均从货币市场账户进行。代理商希望在消费效用的[0,infinity)上最大化预期的折扣积分。我们以lambda1 / 3的幂计算值函数的渐近展开。
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