Igor Cialenco

ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter

Approximation of stochastic partial differential equations by a kernel-based collocation method

H\geq 1/2

Dynamic Coherent Acceptability Indices and Their Applications to Finance

. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation.

Dynamic Assessment Indices

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations (SPDEs). Using an implicit time-stepping scheme, we transform stochastic parabolic equations into stochastic elliptic equations. Our main attention is concentrated on the numerical solution of the elliptic equations at each time step. The estimator of the solution of the elliptic equations is given as a linear combination of reproducing kernels derived from the differential and boundary operators of the SPDE centred at collocation points to be chosen by the user. The random expansion coefficients are computed by solving a random system of linear equations. Numerical experiments demonstrate the feasibility of the method.

PARAMETER ESTIMATIONS FOR SPDES WITH MULTIPLICATIVE FRACTIONAL NOISE

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of so called dynamically consistent sequence of sets of probability measures. Based on these results, we give a specific construction of dynamic coherent acceptability indices. We also provide examples of dynamic coherent acceptability indices, both abstract and also some that generalize selected classical financial measures of portfolio performance.

DO TECHNICAL TRADING PROFITS REMAIN IN THE FOREIGN EXCHANGE MARKET? EVIDENCE FROM FOURTEEN CURRENCIES

This paper provides a unified framework, which allows, in particular, to study the structure of dynamic monetary risk measures and dynamic acceptability indices. The main mathematical tool, which we use here, allows us to significantly generalize existing results is the theory of -modules. In the first part of the paper we develop the general theory and provide a robust representation of conditional assessment indices, and in the second part we apply this theory to dynamic acceptability indices acting on stochastic processes.

Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices

We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter

Collateralized Cva Valuation With Rating Triggers And Credit Migrations

H\in(0,1)

Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations

. Two classes of estimators are investigated: traditional maximum likelihood type estimators, and a new class called closed-form exact estimators. Finally the general results are applied to stochastic heat equation driven by a fractional Brownian motion.

The Reaction of Term Structure of Interest Rates to the Monetary Policy Actions

We examine the in- and out-of-sample behavior of two popular trading systems, Alexander and Double MA filters, for 14 developed-country currencies using daily data with bid-ask spreads. We find significant in-sample returns in the early periods. But out-of-sample returns are lower and only occasionally significant. We show that a currency risk factor proposed in the literature is systematically related to these returns. We find no support for the hypotheses that falling transactions costs are responsible for declining trading profits or for the Adaptive Market hypothesis. Importantly, we show that algorithms that simulate out-of-sample returns have serious instability difficulties.