Herein, we develop a backward stochastic differential equation (BSDE) valuation of securities with default risk. Consequently, the optimal recovery problem with quasi-linear utility functions is discussed with the help of the stochastic maximum principle. Finally, two important examples: the exponential and power utility cases are studied and their business implications are considered.
Let be a finite group. We prove that if every self-centralizing subgroup of is nilpotent or subnormal or a TI-subgroup, then every subgroup of is nilpotent or subnormal. Moreover, has either a normal Sylow -subgroup or a normal -complement for each prime divisor of .
We address a queueing control problem considering service times and conversion times following normal distributions. We formulate the multi-server queueing control problem by constructing a semi-Markov decision process (SMDP) model. The mechanism of state transitions is developed through mathematical derivation of the transition probabilities and transition times. We also study the property of the queueing control system and show that optimizing the objective function of the addressed queueing control...
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