We study the optimal investment problem in a constrained financial market,where the proportion of borrowed amount to the current wealth level is no more than a given constant. The objective is to maximize the goal-reaching probability before drawdown,namely,the probability that the value of the wealth process reaches the safe level before hitting a lower dynamic barrier. The financial market consists of a risk-free asset and multiple risky assets. By the construction of auxiliary market and convex analysis,we relax the borrowing constraint and investigate the new optimization problem in an auxiliary market,where there is no such borrowing constraint. Then,we find the relationship between the optimal results in auxiliary market and those in constrained market. The explicit expressions for the optimal investment strategy and the maximum goal-reaching probability before drawdown are derived in closed-form. Finally,we provide some numerical examples to show the effect of model parameters on the behaviors of investor.
Citation: Yu Yuan, Qicai Li. Maximizing the goal-reaching probability before drawdown with borrowing constraint[J]. AIMS Mathematics, 2021, 6(8): 8868-8882. doi: 10.3934/math.2021514
We study the optimal investment problem in a constrained financial market,where the proportion of borrowed amount to the current wealth level is no more than a given constant. The objective is to maximize the goal-reaching probability before drawdown,namely,the probability that the value of the wealth process reaches the safe level before hitting a lower dynamic barrier. The financial market consists of a risk-free asset and multiple risky assets. By the construction of auxiliary market and convex analysis,we relax the borrowing constraint and investigate the new optimization problem in an auxiliary market,where there is no such borrowing constraint. Then,we find the relationship between the optimal results in auxiliary market and those in constrained market. The explicit expressions for the optimal investment strategy and the maximum goal-reaching probability before drawdown are derived in closed-form. Finally,we provide some numerical examples to show the effect of model parameters on the behaviors of investor.
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