123,173 research outputs found
Dual representations for general multiple stopping problems
In this paper, we study the dual representation for generalized multiple
stopping problems, hence the pricing problem of general multiple exercise
options. We derive a dual representation which allows for cashflows which are
subject to volume constraints modeled by integer valued adapted processes and
refraction periods modeled by stopping times. As such, this extends the works
by Schoenmakers (2010), Bender (2011a), Bender (2011b), Aleksandrov and Hambly
(2010), and Meinshausen and Hambly (2004) on multiple exercise options, which
either take into consideration a refraction period or volume constraints, but
not both simultaneously. We also allow more flexible cashflow structures than
the additive structure in the above references. For example some exponential
utility problems are covered by our setting. We supplement the theoretical
results with an explicit Monte Carlo algorithm for constructing confidence
intervals for the price of multiple exercise options and exemplify it by a
numerical study on the pricing of a swing option in an electricity market.Comment: This is an updated version of WIAS preprint 1665, 23 November 201
Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes
Fast pricing of American-style options has been a difficult problem since it
was first introduced to financial markets in 1970s, especially when the
underlying stocks' prices follow some jump-diffusion processes. In this paper,
we propose a new algorithm to generate tight upper bounds on the Bermudan
option price without nested simulation, under the jump-diffusion setting. By
exploiting the martingale representation theorem for jump processes on the dual
martingale, we are able to explore the unique structure of the optimal dual
martingale and construct an approximation that preserves the martingale
property. The resulting upper bound estimator avoids the nested Monte Carlo
simulation suffered by the original primal-dual algorithm, therefore
significantly improves the computational efficiency. Theoretical analysis is
provided to guarantee the quality of the martingale approximation. Numerical
experiments are conducted to verify the efficiency of our proposed algorithm
From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments
We consider a non-stochastic online learning approach to price financial
options by modeling the market dynamic as a repeated game between the nature
(adversary) and the investor. We demonstrate that such framework yields
analogous structure as the Black-Scholes model, the widely popular option
pricing model in stochastic finance, for both European and American options
with convex payoffs. In the case of non-convex options, we construct
approximate pricing algorithms, and demonstrate that their efficiency can be
analyzed through the introduction of an artificial probability measure, in
parallel to the so-called risk-neutral measure in the finance literature, even
though our framework is completely adversarial. Continuous-time convergence
results and extensions to incorporate price jumps are also presented
Low Power Dynamic Scheduling for Computing Systems
This paper considers energy-aware control for a computing system with two
states: "active" and "idle." In the active state, the controller chooses to
perform a single task using one of multiple task processing modes. The
controller then saves energy by choosing an amount of time for the system to be
idle. These decisions affect processing time, energy expenditure, and an
abstract attribute vector that can be used to model other criteria of interest
(such as processing quality or distortion). The goal is to optimize time
average system performance. Applications of this model include a smart phone
that makes energy-efficient computation and transmission decisions, a computer
that processes tasks subject to rate, quality, and power constraints, and a
smart grid energy manager that allocates resources in reaction to a time
varying energy price. The solution methodology of this paper uses the theory of
optimization for renewal systems developed in our previous work. This paper is
written in tutorial form and develops the main concepts of the theory using
several detailed examples. It also highlights the relationship between online
dynamic optimization and linear fractional programming. Finally, it provides
exercises to help the reader learn the main concepts and apply them to their
own optimizations. This paper is an arxiv technical report, and is a
preliminary version of material that will appear as a book chapter in an
upcoming book on green communications and networking.Comment: 26 pages, 10 figures, single spac
Robust One Period Option Modelling
AMS classifications: 90C15; 90C20; 90C90; 49M29;return on investment;option pricing models;optimization;portfolio investment
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
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