A crash course in stochastic calculus with applications to mathematical finance

A Jane Street Trading Mock Interview with Graham and Andrea
A Jane Street Trading Mock Interview with Graham and Andrea

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1996

Stochastic Processes and their Applications

Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading

1999 •

Applied Mathematics & Optimization

Forward equations for reflected diffusions with jumps

1996 •

Mathematics of Operations Research

Approximating Martingales for Variance Reduction in Markov Process Simulation

2002 •

2003 •

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be in‡uenced by the uncertainty of exit time? In order to answer that question, we consider a suitable extension of the familiar optimal investment problem of Merton (1971), where we allow the conditional distribution function of an agent's time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we show that the portfolio decision is aected. For CRRA preferences, we also show that a solution formally similar to the one obtained in the case of a constant time-horizon can be recovered at the cost of a suitable adjustment to the drift process of the risky assets.

The Annals of Probability

Explicit form and robustness of martingale representations

2000 •

2002 •

We generalize the notion of Brownian bridge. More precisely, we study a standard Brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations that we call conditioned stochastic differential equations.

2000 •

Stochastic processes are becoming more important to actuaries: they underlie much of modern …nance, mortality analysis and general insurance; and they are reappearing in the actuarial syllabus. They are immensely useful, not because they lead to more advanced mathematics (though they can do that) but because they form the common language of workers in many areas that overlap actuarial science. It is precisely because most …nancial and insurance risks involve events unfolding as time passes that models based on processes turn out to be most natural. This paper is an introduction to the language of stochastic processes. We do not give rigorous de…nitions or derivations; our purpose is to introduce the vocabulary, and then survey some applications in life insurance, …nance and general insurance.

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Infinite Dimensional Analysis, Quantum Probability and Related Topics

REGULAR GENERALIZED FUNCTIONS IN GAUSSIAN ANALYSIS

1999 •

Stochastic Processes and their Applications

A partial introduction to financial asset pricing theory

2001 •

Stochastic Processes and their Applications

n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes

2003 •

Stochastic Processes and their Applications

A general problem of an optimal equivalent change of measure and contingent claim pricing in an incomplete market

2000 •

Probability Theory and Related Fields

Rescaled contact processes converge to super-Brownian motion in two or more dimensions

1999 •

Stochastic Processes and their Applications

On confined McKean Langevin processes satisfying the mean no-permeability boundary condition

2011 •

Stochastic Processes and their Applications

Weak convergence to the multiple Stratonovich integral

2000 •

Stochastic Processes and their Applications

Progressive enlargement of filtrations with initial times

2009 •

Stochastic Processes and their Applications

Strong approximations of additive functionals of a planar Brownian motion

2004 •

Stochastics An International Journal of Probability and Stochastic Processes

On the differentiation of heat semigroups and poisson integrals

1997 •

2007 •

1999 •

Stochastic Processes and their Applications

Regularization of differential equations by fractional noise

2002 •

Probability Theory and Related Fields

Brownian motion and the formation of singularities in the heat flow for harmonic maps

1996 •

Annales de l’Institut Henri Poincaré, Probabilités et Statistiques

Variational representations for continuous time processes

2011 •

Probability Theory and Related Fields

Solving forward-backward stochastic differential equations explicitly ? a four step scheme

1994 •

SSRN Electronic Journal

Immersion Property and Credit Risk Modeling

2000 •

Annales de l’Institut Henri Poincare (B) Probability and Statistics

On weak Brownian motions of arbitrary order

2000 •

Applied Mathematics and Optimization

Boundary Sensitivities for Diffusion Processes in Time Dependent Domains

2006 •

Stochastic Processes and their Applications

An approximation result for a nonlinear Neumann boundary value problem via BSDEs

2004 •

Mathematical Finance

Mean-Variance Hedging for Stochastic Volatility Models

2000 •

2010 •

2006 •

The Annals of Applied Probability

Reflected BSDEs when the obstacle is not right-continuous and optimal stopping

2004 •

Statistica Neerlandica

Understanding limit theorems for semimartingales: a short survey

2010 •

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