A stochastic mesh method for pricing high-dimensional American options

We consider a consistent test, that is similar to a Kolmogorov-Smirnov test, of the complete set of restrictions that relate to the copula representation of positive quadrant dependence. For such a test we propose and justify inference relying on a simulation based multiplier method and a bootstrap method. We also explore the finite sample behaviour of both methods with Monte Carlo experiments. A first empirical illustration is given for US insurance claim data. A second one examines the presence of positive quadrant dependence in life expectancies at birth of males and females among countries.

A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence

Thank you very much for reading introduction to stochastic calculus applied to finance. Maybe you have knowledge that, people have search numerous times for their favorite readings like this introduction to stochastic calculus applied to finance, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they are facing with some malicious virus inside their laptop.

Introduction To Stochastic Calculus Applied To Finance

This article has no abstract.

Keywords:

actuarial journals;
insurance mathematics;
insurance economics

Insurance: Mathematics and Economics

If {Pθ}, θ e Ω, be a family of probability measures on an abstract sample space S and T be a sufficient statistic for θ then for a statistic T1 to be stochastically independent of T it is necessary that the probability distribution of T1 be independent of θ. The condition is also sufficient if T be a boundedly complete sufficient statistic. Certain well-known results of distribution theory follow immediately from the above considerations. For instance, if x1, x2,..., xn, are independent N(μ, σ)’s then the sample mean x and the sample variance s2 are mutually independent and are jointly independent of any statistic f (real or vector valued) that is independent of change of scale and origin. It is also deduced that if x1, x2,..., xn are independent random variables such that their joint distribution involves an unknown location parameter θ then there can exist a linear boundedly complete sufficient statistic for θ only if the x’s are all normal.Similar characterizations for the Gamma distribution also are indicated.

Statistics Independent of a Complete Sufficient Statistic

Informative frequency band selection in the presence of non-Gaussian noise – a novel approach based on the conditional variance statistic with application to bearing fault diagnosis

We propose a method for defining and measuring spatial contagion between two financial markets via conditional copulas. Some theoretical results on monotonicity and asymptotic properties of Gaussian copulas with respect to conditioning are presented. Next, we combine the spatial contagion approach with time series models. We investigate which model from a large family of multivariate GARCH is the best tool for modelling spatial contagion. In an empirical study, we show that among models designed for general fit, a two-step model fitting procedure reduces the ability to describe the contagion effect. This is a feature of copula-GARCH models. Copyright © 2013 John Wiley & Sons, Ltd.

On spatial contagion and multivariate GARCH models

In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the LM-measure and the notion of the update rule that, we believe, are the key tools for studying time consistency in a unified framework.

A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

/pdf/a-survey-of-time-consistency-of-dynamic-risk-measures-and-3p3hqqr80n.pdf

The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures of risk measures in terms of bias. We show that once the parameters of a model need to be estimated, one has to take additional care when estimating risks. The typical plug-in approach, for example, introduces a bias which leads to a systematic underestimation of risk. In this regard, we introduce a novel notion of unbiasedness to the estimation of risk which is motivated by economic principles. In general, the proposed concept does not coincide with the well-known statistical notion of unbiasedness. We show that an appropriate bias correction is available for many well-known estimators. In particular, we consider value-at-risk and expected shortfall (tail value-at-risk). In the special case of normal distributions, closed-formed solutions for unbiased estimators can be obtained. We present a number of motivating examples which show the outperformance of unbiased estimators in many circumstances. The unbiasedness has a direct impact on backtesting and therefore adds a further viewpoint to established statistical properties.

/pdf/unbiased-estimation-of-risk-2umk166yvx.pdf

Marcin Pitera

Papers

Informative frequency band selection in the presence of non-Gaussian noise – a novel approach based on the conditional variance statistic with application to bearing fault diagnosis

On spatial contagion and multivariate GARCH models

A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

Unbiased estimation of risk