On best proximity pair theorems and fixed-point theorems.
On Bilevel Variational Inequalities Arising in the Analysis of Improper Optimization Problems
On Carathéodory's and Krein-Milman's theorems in fully ordered groups
On certain aspects of generative grammar computer testing
On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.
We obtain a closed formula for the Laplace transform of the first moment of certain exponential functionals of Brownian motion with drift, which gives the price of Asian options. The proof relies on an identity in law between the average on [0,t] of a geometric Brownian motion and the value at time t of a Markov process, for which we can compute explicitly the resolvent.
On computer-aided solving differential equations and stability study of markets.
On Conditional Value at Risk (CoVaR) for tail-dependent copulas
The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.
On convex combinations of two values
We study values for cooperative TU-games which are convex combinations of the Shapley value and the solidarity value, introduced in our recent paper [1]. First, we axiomatize the convex combination of the two values in the case when the coefficients are given exogenously. Next, we give an axiomatic description of the whole family of such values.
On cooperative games connected with markets
On decidability of skeletal sets [Abstract of thesis]
On decision-making in possibility theory
We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision...
On detectors with incomplete answers
On determining sets for the class of somewhat continuous functions
On estimating the yield and volatility curves
On European option pricing under partial information
We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...
On exact null controllability of Black-Scholes equation
In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with ...
On existence of equilibrium pair for constrained generalized games.
On game ideals
On games of Topsoe.
On Generalized Bellman 's Functional Equation.