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We study the feedback effects induced by portfolio optimizers on the underlying asset prices. Through their interaction with reference traders, who trade based on some aggregate incomes process, they are assumed to move asset prices away from the standard log-normal model. With market clearing as our main constraint, we solve analytically for the… (More)
We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in certain cases. The accuracy and high-resolution properties of our scheme… (More)
We propose a method for calibrating a volatility surface that matches option prices using an entropy-inspired framework. Starting with a stochastic volatility model for asset prices, we cast the estimation problem as a variational one and we derive a Hamilton-Jacobi-Bellman (HJB) equation for the volatility surface. We study the asymptotics of the HJB… (More)
This paper extends a result obtained by Wigner and von Neu-mann. We prove that a non-constant real-valued function, f (x), in C 3 (I) where I is an interval of the real line, is a monotone matrix function of order n + 1 on I if and only if a related, modified function gx 0 (x) is a monotone matrix function of order n for every value of x 0 in I, assuming… (More)
Through the issuance of equity-linked insurance policies, insurance companies are increasingly facing losses that have heavy exposure to capital market risks. In this paper, we determine the continuous premium rate that an insurer exposed to such risks charges via the principle of equivalent utility. Using exponential utility, we obtain the resulting… (More)
Regenerating skin, growing new organs—molecular and cellular biology promise surprising advances in medical science. What about consciousness? Old questions and new approaches in the farthest frontier of neuroscience.