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In this paper, we investigate an optimal asset allocation problem in a financial market consisting of one risk-free asset, one liquid risky asset and one illiquid risky asset. The liquidity risk stems from the asset that cannot be traded continuously, and the trading opportunities are captured by a Poisson process with constant intensity. Also, it is assumed that the interest rate is stochastically varying and follows the Cox–Ingersoll–Ross model. The performance functional of the decision maker is selected as the expected logarithmic utility of the total wealth at terminal time. The dynam...

This paper proposes Parisian and Parasian default mechanics for modeling the credit risks of the CDS (credit default swap) contracts. Unlike most of the structural models used in the literature, our new model assumes that the default will occur only if the price of the reference asset stays below a certain level for a pre-described period of time. To work out the corresponding CDS price, a general pricing formula containing the unknown no-default probability is derived first. It is then shown that the determination of such a probability is equivalent to the valuation of a Parisian or Parasian ...