214 research outputs found
Affine Processes and Application in Finance
We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.
No-arbitrage in discrete-time markets with proportional transaction costs and general information structure
We discuss the no-arbitrage conditions in a general framework for
discrete-time models of financial markets with proportional transaction costs
and general information structure. We extend the results of Kabanov and al.
(2002), Kabanov and al. (2003) and Schachermayer (2004) to the case where
bid-ask spreads are not known with certainty. In the "no-friction" case, we
retrieve the result of Kabanov and Stricker (2003)
No arbitrage and closure results for trading cones with transaction costs
In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, , does obey the fundamental theorem of asset pricing and, secondly, if is arbitrage-free then it is the closure of . We then conclude by showing how to represent claims
The dual optimizer for the growth-optimal portfolio under transaction costs
We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar et al.(Math. Oper. Res. 13:277-294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341-1358, 2010) for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows one to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rat
European Options in a Nonlinear Incomplete Market Model with Default
We study the superhedging prices and the associated superhedging strategies for European options in a nonlinear incomplete market model with default. The underlying market model consists of one risk-free asset and one risky asset, whose price may admit a jump at the default time. The portfolio processes follow nonlinear dynamics with a nonlinear driver . By using a dynamic programming approach, we first provide a dual formulation of the seller's (superhedging) price for the European option as the supremum, over a suitable set of equivalent probability measures , of the -evaluation/expectation under of the payoff. We also establish a characterization of the seller's (superhedging) price as the initial value of the minimal supersolution of a constrained backward stochastic differential equation with default. Moreover, we provide some properties of the terminal profit made by the seller, and some results related to replication and no-arbitrage issues. Our results rely on first establishing a nonlinear optional and a nonlinear predictable decomposition for processes which are -strong supermartingales under for all
Mutual Fund Theorem for continuous time markets with random coefficients
We study the optimal investment problem for a continuous time incomplete
market model such that the risk-free rate, the appreciation rates and the
volatility of the stocks are all random; they are assumed to be independent
from the driving Brownian motion, and they are supposed to be currently
observable. It is shown that some weakened version of Mutual Fund Theorem holds
for this market for general class of utilities; more precisely, it is shown
that the supremum of expected utilities can be achieved on a sequence of
strategies with a certain distribution of risky assets that does not depend on
risk preferences described by different utilities.Comment: 17 page
Arbitrage and deflators in illiquid markets
This paper presents a stochastic model for discrete-time trading in financial
markets where trading costs are given by convex cost functions and portfolios
are constrained by convex sets. The model does not assume the existence of a
cash account/numeraire. In addition to classical frictionless markets and
markets with transaction costs or bid-ask spreads, our framework covers markets
with nonlinear illiquidity effects for large instantaneous trades. In the
presence of nonlinearities, the classical notion of arbitrage turns out to have
two equally meaningful generalizations, a marginal and a scalable one. We study
their relations to state price deflators by analyzing two auxiliary market
models describing the local and global behavior of the cost functions and
constraints
Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem
In this paper, we study a class of quadratic Backward Stochastic Differential
Equations (BSDEs) which arises naturally when studying the problem of utility
maximization with portfolio constraints. We first establish existence and
uniqueness results for such BSDEs and then, we give an application to the
utility maximization problem. Three cases of utility functions will be
discussed: the exponential, power and logarithmic ones
Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models
We consider a class of generalized capital asset pricing models in continuous
time with a finite number of agents and tradable securities. The securities may
not be sufficient to span all sources of uncertainty. If the agents have
exponential utility functions and the individual endowments are spanned by the
securities, an equilibrium exists and the agents' optimal trading strategies
are constant. Affine processes, and the theory of information-based asset
pricing are used to model the endogenous asset price dynamics and the terminal
payoff. The derived semi-explicit pricing formulae are applied to numerically
analyze the impact of the agents' risk aversion on the implied volatility of
simultaneously-traded European-style options.Comment: 24 pages, 4 figure
Cotauberian Operators on L1(0, 1) Obtained by Lifting
ABSTRACT:We show that the set Td(L1(0, 1)) of cotauberian operators acting on L1(0, 1) is not open, and T ? Td(L1(0, 1)) does not imply T** cotauberian. As a consequence, we derive that the set T(L8(0, 1)) of tauberian operators acting on L8(0, 1) is not open, and that T ? T(L8(0,1)) does not imply T** tauberian
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