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Keywords
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Itô’s formula, Optimal Strategy, Portfolio optimization, Defaultable security, Credit risk, Recovery of market value.
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Abstract
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In this paper, we obtain a closed-form solution for a diffusion risk model which optimally
allocates his/her wealth among the following coffecients: a risky asset, a free bank account,
and a stock. The following relationships between the optimal amount invested in the security
and the risk premium are obtained: (i) for a risk premium greater than one, the investor will
optimally invest a positive amount in the bond, and (ii) for a risk premium equal to one, the
insurance company will optimally invest nothing in the bond. Although the inclusion of a
credit-related financial product in the portfolio selection if risk models is more realistic, no
closed-form solutions to date are given in the literature when a recovery value is considered
in the event of a default. We solve the optimal portfolio problem of insurance company for
the representative investor with a specified utility function. Moreover, the implications of
the analytic result for asset allocation are discussed and carried out sensitivity analysis by
adopting benchmark parameter values.
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