Optimal investment consumption model with a higher interest rate for borrowing
The paper considers a consumption-investment model for a single agent. The investor consumes the wealth \(X(t)\) at a nonnegative rate \(c(t)\) and distributes it between one riskless bond with instantaneous rate of return \(r\) and the \(d\) risk stocks whose prices are driven by a Wiener process. Stock purchases may be financed by borrowing at a higher interest rate \(R\geq r\#.\) The authors include also the dividend rate even in the case when \(R>r\) and it is the characteristic feature of the paper. The usual optimization problem with two utility functions is formulated, and a family of auxiliary optimization problems is introduced. A solution of the original problem is presented via the properties of the solutions of auxiliary problems. By using duality methods, the existence of optimal portfolio consumption is proved, and the explicit solution leading to feedback formulae are derived for deterministic coefficients.
scientific article; zbMATH DE number 1542577