63 research outputs found
On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation
A typical approach to tackle stochastic control problems with partial
observation is to separate the control and estimation tasks. However, it is
well known that this separation generally fails to deliver an actual optimal
solution for risk-sensitive control problems. This paper investigates the
separability of a general class of risk-sensitive investment management
problems when a finite-dimensional filter exists. We show that the
corresponding separated problem, where instead of the unobserved quantities,
one considers their conditional filter distribution given the observations, is
strictly equivalent to the original control problem. We widen the applicability
of the so-called Modified Zakai Equation (MZE) for the study of the separated
problem and prove that the MZE simplifies to a PDE in our approach.
Furthermore, we derive criteria for separability. We do not solve the separated
control problem but note that the existence of a finite-dimensional filter
leads to a finite state space for the separated problem. Hence, the difficulty
is equivalent to solving a complete observation risk-sensitive problem. Our
results have implications for existing risk-sensitive investment management
models with partial observations in that they establish their separability.
Their implications for future research on new applications is mainly to provide
conditions to ensure separability
Arbitrage concepts under trading restrictions in discrete-time financial markets
In a discrete-time setting, we study arbitrage concepts in the presence of
convex trading constraints. We show that solvability of portfolio optimization
problems is equivalent to absence of arbitrage of the first kind, a condition
weaker than classical absence of arbitrage opportunities. We center our
analysis on this characterization of market viability and derive versions of
the fundamental theorems of asset pricing based on portfolio optimization
arguments. By considering specifically a discrete-time setup, we simplify
existing results and proofs that rely on semimartingale theory, thus allowing
for a clear understanding of the foundational economic concepts involved. We
exemplify these concepts, as well as some unexpected situations, in the context
of one-period factor models with arbitrage opportunities under borrowing
constraints.Comment: 29 pages, 1 figur
Large portfolio losses: A dynamic contagion model
Using particle system methodologies we study the propagation of financial
distress in a network of firms facing credit risk. We investigate the
phenomenon of a credit crisis and quantify the losses that a bank may suffer in
a large credit portfolio. Applying a large deviation principle we compute the
limiting distributions of the system and determine the time evolution of the
credit quality indicators of the firms, deriving moreover the dynamics of a
global financial health indicator. We finally describe a suitable version of
the "Central Limit Theorem" useful to study large portfolio losses. Simulation
results are provided as well as applications to portfolio loss distribution
analysis.Comment: Published in at http://dx.doi.org/10.1214/08-AAP544 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A stochastic control perspective on term structure models with roll-over risk
In this paper, we consider a generic interest rate market in the presence of
roll-over risk, which generates spreads in spot/forward term rates. We do not
require classical absence of arbitrage and rely instead on a minimal market
viability assumption, which enables us to work in the context of the benchmark
approach. In a Markovian setting, we extend the control theoretic approach of
Gombani & Runggaldier (2013) and derive representations of spot/forward spreads
as value functions of suitable stochastic optimal control problems, formulated
under the real-world probability and with power-type objective functionals. We
determine endogenously the funding-liquidity spread by relating it to the
risk-sensitive optimization problem of a representative investor.Comment: 22 page
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