Optimal singular control strategies for controlling a process to a goal.
The problem addressed in the paper is to find an optimal strategy, which consists of an optimal choice of a risky asset and allocation of wealth, to maximize the probability of reaching a given total wealth of \(a\) which is strictly larger than the initial condition. The amount invested in the risky asset is given by an Ito process with infinitesimal parameters \(\mu \) and \(\sigma \). At time \(t\), the choice of the risky asset is represented by \(\mu (t)\) and \(\sigma (t)\), which comes from a control set depending on the investor's wealth in the risky asset. At any time wealth can be transferred between the risky asset and a bank account with no transaction fee as long as the transaction process is of bounded variation.
scientific article; zbMATH DE number 1792536
scientific article