We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions...

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the...

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a...

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In particular, the compact schemes of Rigal are generalized. The numerical results are compared to standard...

In Farrell and Maskin (1989), the authors present sufficient conditions for weakly renegotiation-proof payoffs in their Theorem 1 (p. 332). We show that a step in the proof of this theorem is not correct by giving a counterexample. Nevertheless, the sufficient conditions remain true, and we...

As the American early exercise results in a free boundary problem, in this article we add a penalty term to obtain a partial differential equation, and we also focus on an improved definition of the penalty term for American options. We replace the constant penalty parameter with a...

Increasing concerns about climate change have given rise to the formation of International Environmental Agreements (IEAs) as a possible solution to limit global pollution eff ects. In this paper, we study the stability of IEAs in a repeated game framework where we restrict to strategies which...

Increasing concerns about climate change have given rise to the formation of International Environmental Agreements (IEAs) as a possible solution to limit global pollution effects. In this paper, we study the stability of IEAs in a repeated game framework where we restrict to strategies which...

Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic...