Document Type : Research Article
Author
Department of Mathematics and Computer Science, Lorestan University, Lorestan, Iran.
Abstract
In this paper, the credit risk of investment is managed by a new structural mean-reverting model. For this purpose, the utility maximization problem is expressed as an optimization problem with an expected logarithmic objective function and a mean-reverting constraint. The existence of a solution to the expressed problem is proved in a lemma. Moreover, one theorem for facilitating the optimal strategy design algorithm is proved. In this way, the optimal strategy is obtained for hedging the credit risk of investing in stocks of companies. Finally, the distance to default of investment is calculated by using the Black-Scholes formula for call options on wealth values obtained by optimal portfolio selection based on the proposed the optimal strategy. Also, the stability of the proposed method is proved in the second theorem. For demonstrating the applicable results, the portfolio allocation problem is simulated by using the proposed method and compared with the non-mean-reverting equity approach. According to the simulation result, the portfolio values don’t fall and default doesn’t occur during the investment period [0, T], approximately. Also, distance to default tends to zero. period [0, T], approximately. Also, distance to default tends to zero.
Keywords
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