Related papers: Variance optimal hedging for continuous time addit…
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We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number…
In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options…
The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…
We establish differentiability properties of the value function of problems of Static Optimization in an abstract infinite dimensional setting and we apply that to problems of Calculus of Variations. We lighten the assumptions of existing…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
Volatility estimation is a central problem in financial econometrics, but becomes particularly challenging when jump activity is high, a phenomenon observed empirically in highly traded financial securities. In this paper, we revisit the…
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation,…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…
For a mixed stochastic differential equation containing both Wiener process and a H\"older continuous process with exponent $\gamma>1/2$, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of…
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…
We propose two variants of the Smith-Wilson method for practical application in the insurance industry. Our first variant relaxes the Smith-Wilson energy and can be used to incorporate less reliable market data with a certain weight rather…
The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…
This paper presents a numerical model to solve the problem of cash accumulation strategies for products with an unknown future price, like assets. Stock prices are modeled by a discretized Wiener Process, and by the means of ordinary…