37,359 research outputs found
Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach
This paper investigates optimal portfolio strategies in a market where the
drift is driven by an unobserved Markov chain. Information on the state of this
chain is obtained from stock prices and expert opinions in the form of signals
at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl.
Finance, 15, No. 1, we use stochastic filtering to transform the original
problem into an optimization problem under full information where the state
variable is the filter for the Markov chain. The dynamic programming equation
for this problem is studied with viscosity-solution techniques and with
regularization arguments.Comment: 31 page
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
LIBOR additive model calibration to swaptions markets
In the current paper, we introduce a new calibration methodology for the LIBOR market model
driven by LIBOR additive processes based in an inverse problem. This problem can be splitted
in the calibration of the continuous and discontinuous part, linking each part of the problem
with at-the-money and in/out -of -the-money swaption volatilies. The continuous part is based
on a semidefinite programming (convex) problem, with constraints in terms of variability or
robustness, and the calibration of the Lévy measure is proposed to calibrate inverting the
Fourier Transform
Optimal investment under multiple defaults risk: A BSDE-decomposition approach
We study an optimal investment problem under contagion risk in a financial
model subject to multiple jumps and defaults. The global market information is
formulated as a progressive enlargement of a default-free Brownian filtration,
and the dependence of default times is modeled by a conditional density
hypothesis. In this Ito-jump process model, we give a decomposition of the
corresponding stochastic control problem into stochastic control problems in
the default-free filtration, which are determined in a backward induction. The
dynamic programming method leads to a backward recursive system of quadratic
backward stochastic differential equations (BSDEs) in Brownian filtration, and
our main result proves, under fairly general conditions, the existence and
uniqueness of a solution to this system, which characterizes explicitly the
value function and optimal strategies to the optimal investment problem. We
illustrate our solutions approach with some numerical tests emphasizing the
impact of default intensities, loss or gain at defaults and correlation between
assets. Beyond the financial problem, our decomposition approach provides a new
perspective for solving quadratic BSDEs with a finite number of jumps.Comment: Published in at http://dx.doi.org/10.1214/11-AAP829 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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