1,104 research outputs found
On a stochastic differential equation arising in a price impact model
We provide sufficient conditions for the existence and uniqueness of
solutions to a stochastic differential equation which arises in a price impact
model. These conditions are stated as smoothness and boundedness requirements
on utility functions or Malliavin differentiability of payoffs and endowments.Comment: 20 pages. Keywords: Clark-Ocone formula, large investor, Malliavin
derivative, Pareto allocation, price impact, Sobolev's embedding, stochastic
differential equation; a couple of minor editorial corrections to make it
identical to the paper accepted to Stochastic Processes and Their
Application
Flash flood simulation of the Toga River caused by localized torrential rain in urbanized area
River engineeringNumerical modelling in river engineerin
Absolute Continuity Theorem for Random Dynamical Systems on
In this article we provide a proof of the so called absolute continuity
theorem for random dynamical systems on which have an invariant
probability measure. First we present the construction of local stable
manifolds in this case. Then the absolute continuity theorem basically states
that for any two transversal manifolds to the family of local stable manifolds
the induced Lebesgue measures on these transversal manifolds are absolutely
continuous under the map that transports every point on the first manifold
along the local stable manifold to the second manifold, the so-called
Poincar\'e map or holonomy map. In contrast to known results, we have to deal
with the non-compactness of the state space and the randomness of the random
dynamical system.Comment: 46 page
Path regularity and explicit convergence rate for BSDE with truncated quadratic growth
We consider backward stochastic differential equations with drivers of
quadratic growth (qgBSDE). We prove several statements concerning path
regularity and stochastic smoothness of the solution processes of the qgBSDE,
in particular we prove an extension of Zhang's path regularity theorem to the
quadratic growth setting. We give explicit convergence rates for the difference
between the solution of a qgBSDE and its truncation, filling an important gap
in numerics for qgBSDE. We give an alternative proof of second order Malliavin
differentiability for BSDE with drivers that are Lipschitz continuous (and
differentiable), and then derive an analogous result for qgBSDE.Comment: 30 page
Pricing and hedging of derivatives based on non-tradable underlyings
This paper is concerned with the study of insurance related derivatives on
financial markets that are based on non-tradable underlyings, but are
correlated with tradable assets. We calculate exponential utility-based
indifference prices, and corresponding derivative hedges. We use the fact that
they can be represented in terms of solutions of forward-backward stochastic
differential equations (FBSDE) with quadratic growth generators. We derive the
Markov property of such FBSDE and generalize results on the differentiability
relative to the initial value of their forward components. In this case the
optimal hedge can be represented by the price gradient multiplied with the
correlation coefficient. This way we obtain a generalization of the classical
'delta hedge' in complete markets
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