Related papers: Symmetry reductions of a nonlinear option pricing …
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
We investigate upper and lower hedging prices of multivariate contingent claims from the viewpoint of game-theoretic probability and submodularity. By considering a game between "Market" and "Investor" in discrete time, the pricing problem…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
We study scaled trinomial models converging to the Black--Scholes model, and analyze exponential certainty-equivalent prices for path-dependent European options. As the number of trading dates $n$ tends to infinity and the risk aversion is…
Financial markets based on L\'evy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles.…
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that…
In this paper, we focus on the tempered subdiffusive Black-Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing…
In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we prove existence and uniqueness of a solution…
This paper employs a novel Lie symmetries-based framework to model the intrinsic symmetries within financial market. Specifically, we introduce Lie symmetry net (LSN), which characterises the Lie symmetries of the differential equations…
This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their…
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…
An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the…