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On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel, Krishnan Balachandran, Rangarajan Sowrirajan, Jeong-Hoon Kim (2008)

Kybernetika

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 L 2 ...

On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance

Mokhtar Hafayed, Petr Veverka, Syed Abbas (2014)

Applications of Mathematics

We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...

On the Bellman equation for asymptotics of utility from terminal wealth

Janusz Matkowski, Łukasz Stettner (2010)

Applicationes Mathematicae

The asymptotics of utility from terminal wealth is studied. First, a finite horizon problem for any utility function is considered. To study a long run infinite horizon problem, a certain positive homogeneity (PH) assumption is imposed. It is then shown that assumption (PH) is practically satisfied only by power and logarithmic utility functions.

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

German Bernhart, Jan-Frederik Mai, Matthias Scherer (2015)

Dependence Modeling

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper...

Optimal closing of a pair trade with a model containing jumps

Stig Larsson, Carl Lindberg, Marcus Warfheimer (2013)

Applications of Mathematics

A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an...

Optimal investment under behavioural criteria - a dual approach

Miklós Rásonyi, José G. Rodríguez-Villarreal (2015)

Banach Center Publications

We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in Carassus-Rásonyi (2015) under certain conditions on the parameters of these power functions. In the present paper we prove the existence of optimal strategies under a different set of conditions on the parameters, identical to the ones in Rásonyi-Rodrigues (2013), which...

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