62 research outputs found
Stochastic Control Representations for Penalized Backward Stochastic Differential Equations
This paper shows that penalized backward stochastic differential equation
(BSDE), which is often used to approximate and solve the corresponding
reflected BSDE, admits both optimal stopping representation and optimal control
representation. The new feature of the optimal stopping representation is that
the player is allowed to stop at exogenous Poisson arrival times. The
convergence rate of the penalized BSDE then follows from the optimal stopping
representation. The paper then applies to two classes of equations, namely
multidimensional reflected BSDE and reflected BSDE with a constraint on the
hedging part, and gives stochastic control representations for their
corresponding penalized equations.Comment: 24 pages in SIAM Journal on Control and Optimization, 201
Dynkin games with Poisson random intervention times
This paper introduces a new class of Dynkin games, where the two players are
allowed to make their stopping decisions at a sequence of exogenous Poisson
arrival times. The value function and the associated optimal stopping strategy
are characterized by the solution of a backward stochastic differential
equation. The paper further applies the model to study the optimal conversion
and calling strategies of convertible bonds, and their asymptotics when the
Poisson intensity goes to infinity
Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE
In an incomplete market, with incompleteness stemming from stochastic factors
imperfectly correlated with the underlying stocks, we derive representations of
homothetic (power, exponential and logarithmic) forward performance processes
in factor-form using ergodic BSDE. We also develop a connection between the
forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive
optimization. In addition, we develop a connection, for large time horizons,
with a family of classical homothetic value function processes with random
endowments.Comment: 34 page
Analysis of the optimal exercise boundary of American put option with delivery lags
We show that an American put option with delivery lags can be decomposed as a
European put option and another American-style derivative. The latter is an
option for which the investor receives the Greek Theta of the corresponding
European option as the running payoff, and decides an optimal stopping time to
terminate the contract. Based on the this decomposition, we further show that
the associated optimal exercise boundary exists, and is a strictly increasing
and smooth curve. We also analyze its asymptotic behavior for both large
maturity and small time lag using the free-boundary method.Comment: 28 pages, 5 figure
Fully coupled forward-backward stochastic dynamics and functional differential systems
This article introduces and solves a general class of fully coupled
forward-backward stochastic dynamics by investigating the associated system of
functional differential equations. As a consequence, we are able to solve many
different types of forward-backward stochastic differential equations (FBSDEs)
that do not fit in the classical setting. In our approach, the equations are
running in the same time direction rather than in a forward and backward way,
and the conflicting nature of the structure of FBSDEs is therefore avoided.Comment: 24 page
Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs
This paper studies the properties of the optimal portfolio-consumption
strategies in a {finite horizon} robust utility maximization framework with
different borrowing and lending rates. In particular, we allow for constraints
on both investment and consumption strategies, and model uncertainty on both
drift and volatility. With the help of explicit solutions, we quantify the
impacts of uncertain market parameters, portfolio-consumption constraints and
borrowing costs on the optimal strategies and their time monotone properties.Comment: 35 pages, 8 tables, 1 figur
Funding Liquidity, Debt Tenor Structure, and Creditor's Belief: An Exogenous Dynamic Debt Run Model
We propose a unified structural credit risk model incorporating both
insolvency and illiquidity risks, in order to investigate how a firm's default
probability depends on the liquidity risk associated with its financing
structure. We assume the firm finances its risky assets by mainly issuing
short- and long-term debt. Short-term debt can have either a discrete or a more
realistic staggered tenor structure. At rollover dates of short-term debt,
creditors face a dynamic coordination problem. We show that a unique threshold
strategy (i.e., a debt run barrier) exists for short-term creditors to decide
when to withdraw their funding, and this strategy is closely related to the
solution of a non-standard optimal stopping time problem with control
constraints. We decompose the total credit risk into an insolvency component
and an illiquidity component based on such an endogenous debt run barrier
together with an exogenous insolvency barrier.Comment: 36 pages, 9 figures. The article was previously circulated under the
title A Continuous Time Structural Model for Insolvency, Recovery, and
Rollover Risks in Mathematics and Financial Economics, 201
Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints
This paper considers utility indifference valuation of derivatives under
model uncertainty and trading constraints, where the utility is formulated as
an additive stochastic differential utility of both intertemporal consumption
and terminal wealth, and the uncertain prospects are ranked according to a
multiple-priors model of Chen and Epstein (2002). The price is determined by
two optimal stochastic control problems (mixed with optimal stopping time in
the case of American option) of forward-backward stochastic differential
equations. By means of backward stochastic differential equation and partial
differential equation methods, we show that both bid and ask prices are closely
related to the Black-Scholes risk-neutral price with modified dividend rates.
The two prices will actually coincide with each other if there is no trading
constraint or the model uncertainty disappears. Finally, two applications to
European option and American option are discussed.Comment: 28 pages in Science China Mathematics, 201
- …