Mathematics of Financial Obligations

On investment and minimization of shortfall risk for a diffusion model with jumps and two interest rates via market completion

“…The investment problem (see, for instance, Karatzas and Shreve [14], Melnikov et al [17]) consists in finding…”

On pricing contingent claims in a two interest rates jump-diffusion model via market completions

“…define (see Melnikov et al [15]) a density Z of a unique martingale measure P * in the (B, S 1 , S 2 )-market as a stochastic exponent (2.10)…”

“…where E * is the expected value under the risk neutral measure, and [15].) We derive the well-known price of a put option from the call-put parity.…”

Evaluation of the probability of bankruptcy for a model of insurance company

“…This explains the existing high interest to the investigation of this problem discussed in numerous works and monographs (see, e.g., [1,2]). In the present work, we study the problem of evaluation the probability of bankruptcy of an insurance company for infinitely steps in the case where the company can invest its capital to bank deposits at any time.…”