We propose a dynamic structural model of credit risk of multiple loan portfolios. In line with Merton, Vasicek and Pykhtin, we assume that a loan defaults if the assets of the debtor fall below his liabilities, and that the subsequent loss given default is determined by the collateral value. For...

Recently, the continuous double auction, i.e. the trading mechanism used in the majority of the financial markets, is the subject of an extensive study. In the present paper, a model of the continuous double auction with the completely random flow of the limit orders is studied. The main result...

<p><p><span style="font-size: 11.000000pt; font-family: 'CMR10';">We apply stratified sampling with equiprobable strata and a single observa- tion drawn from each stratum to the approximate computation of stochastic programming problems. We determine the convergence rate of the approximation error both when com- puting expectations and when approximating...</span></p></p>

We suggest a model of (a thin) market at which the number of participants is random with Poisson distribution. We provide a formula for joint distribution of the market price and the traded volume. We derive an asymptotic distribution of the quantities. We find that, according to our model, with...

Recently, models of limit order markets, particularly those of the continuous double auction, are subject to an intense research. Due to their complexity, the models are regarded to be analytically intractable. In the present paper, nonetheless, a closed form result is derived: the conditional...

We assume a thin market with finite number of buyers and sellers, each agent having a single jump demand xor supply function (the jump is unit). Further, we assume that number of each agent's arrival is a Poisson distributed random variable. We describe the joint distribution of the market price...

In the paper, the asymptotic distribution of the equilibrium price in markets with the random demand and supply is described. Two special cases - the one with smooth demand and supply curves and the one with jump demand and supply curves - are studied. It is found that in both the cases the...

We propose a dynamic structural model of a loan portfolio, secured by collaterals. Contrary to existing dynamic models, our model takes into account the time-dependence of the debtors' wealth and the fact that, due to defaults, the financial health within the portfolio improves in comparison to...

We introduce a theoretical tool for handling pure-jump processes taking values in complex spaces. We generalize the notion of rate kernels for the non-Markov case, being able to describe any pure-jump process in Borel space with absolutely continuous conditional distribution of jump times. We...

We estimate the tail exponent of daily, weekly and monthly returns of 22 world stocks. We show that the left tails are significantly heavier than the right one. On the other hand, we find indications against the stylized fact that the tails of longer period returns lighter than those of the...