Results 1  10
of
25
Hedging of Defaultable Claims
, 2004
"... Contents 1 Replication of Defaultable Claims 7 1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 DefaultFree Market . . . . . . . . . . . . . . . . . . . . . 8 1.1.2 Random Time . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Defaultable Claims . . . . . . . ..."
Abstract

Cited by 38 (12 self)
 Add to MetaCart
Contents 1 Replication of Defaultable Claims 7 1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 DefaultFree Market . . . . . . . . . . . . . . . . . . . . . 8 1.1.2 Random Time . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Defaultable Claims . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.1 Default Time . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 RiskNeutral Valuation . . . . . . . . . . . . . . . . . . . 13 1.2.3 Defaultable Term Structure . . . . . . . . . . . . . . . . . 15 1.3 Properties of Trading Strategies . . . . . . . . . . . . . . . . . . . 16 1.3.1 DefaultFree Primary Assets . . . . . . . . . . . . . . . . 17 1.3.2 Defaultable and DefaultFree Primary Assets . . . . . . . 23 1.4 Replication of Defaultable Claims . . . . . . . . . . . . . . . . . . 30 1.4.1 Replication of a Promised Payo# . . . . . . . . . . . . . . 30 1.4.2 Replication of a Recovery Payo# . . . . . . . . . . . . . . 34 1.4.3 Replication
continuoustime meanvariance portfolio selection with bankruptcy prohibition.
 Mathematical Finance,
, 2005
"... A continuoustime meanvariance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar am ..."
Abstract

Cited by 28 (5 self)
 Add to MetaCart
A continuoustime meanvariance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a meanvariance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.
A HamiltonJacobiBellman approach to optimal trade execution
, 2009
"... The optimal trade execution problem is formulated in terms of a meanvariance tradeoff, as seen at the initial time. The meanvariance problem can be embedded in a LinearQuadratic (LQ) optimal stochastic control problem, A semiLagrangian scheme is used to solve the resulting nonlinear Hamilton Ja ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
The optimal trade execution problem is formulated in terms of a meanvariance tradeoff, as seen at the initial time. The meanvariance problem can be embedded in a LinearQuadratic (LQ) optimal stochastic control problem, A semiLagrangian scheme is used to solve the resulting nonlinear Hamilton Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparision property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.
Continuoustime Markowitz’s problems in an incomplete market, with noshorting portfolios
, 2005
"... Continuoustime Markowitz’s mean–variance portfolio selection problems with finitetime horizons are investigated in an arbitragefree yet incomplete market. Models with unconstrained and noshorting portfolios are tackled respectively. The sets of the terminal wealths that can be replicated by adm ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Continuoustime Markowitz’s mean–variance portfolio selection problems with finitetime horizons are investigated in an arbitragefree yet incomplete market. Models with unconstrained and noshorting portfolios are tackled respectively. The sets of the terminal wealths that can be replicated by admissible portfolios are characterized in explicit terms. This enables one to transfer the original dynamic portfolio selection problems into ones of static, albeit constrained, optimization problems in terms of the terminal wealth. Solutions to the latter are obtained via certain dual (static) optimization problems. When all the market coefficients are deterministic processes, mean–variance efficient portfolios and frontiers are derived explicitly.
Dynamic Portfolio Selection under CapitalatRisk
, 2003
"... Portfolio optimization under downside risk while preserving the upside is of crucial importance to asset managers. In the BlackScholes setting, we consider one such particular measure given by the notion of capitalatrisk. This paper generalizes the work of Emmer et al., 2001, to the case of time ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Portfolio optimization under downside risk while preserving the upside is of crucial importance to asset managers. In the BlackScholes setting, we consider one such particular measure given by the notion of capitalatrisk. This paper generalizes the work of Emmer et al., 2001, to the case of time dependent parameters and investment strategies, i.e., continuoustime portfolio optimization, and considers furthermore, the additional constraint of noshortselling. Analytical formulae are derived for the optimal strategies, and numerical examples are presented.
STOCHASTIC LINEARQUADRATIC CONTROL WITH CONIC CONTROL CONSTRAINTS ON AN INFINITE TIME HORIZON
, 2004
"... This paper is concerned with a stochastic linearquadratic (LQ) control problem in the infinite time horizon where the control is constrained in a given, arbitrary closed cone, the cost weighting matrices are allowed to be indefinite, and the state is scalarvalued. First, the (meansquare, conic) ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper is concerned with a stochastic linearquadratic (LQ) control problem in the infinite time horizon where the control is constrained in a given, arbitrary closed cone, the cost weighting matrices are allowed to be indefinite, and the state is scalarvalued. First, the (meansquare, conic) stabilizability of the system is defined, which is then characterized by a set of simple conditions involving linear matrix inequalities (LMIs). Next, the issue of wellposedness of the underlying optimal LQ control, which is necessitated by the indefiniteness of the problem, is addressed in great detail, and necessary and sufficient conditions of the wellposedness are presented. On the other hand, to address the LQ optimality two new algebraic equations à la Riccati, called extended algebraic Riccati equations (EAREs), along with the notion of their stabilizing solutions, are introduced for the first time. Optimal feedback control as well as the optimal value are explicitly derived in terms of the stabilizing solutions to the EAREs. Moreover, several cases when the stabilizing solutions do exist are discussed and algorithms of computing the solutions are presented. Finally, numerical examples are provided to illustrate the theoretical results established.
CONVEX DUALITY IN CONSTRAINED MEANVARIANCE PORTFOLIO OPTIMIZATION
"... We apply conjugate duality to establish existence of optimal portfolios in an assetallocation problem, with the goal of minimizing the variance of the final wealth which results from trading over a fixed finite horizon in a continuoustime complete market, subject to the constraints that the expec ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
We apply conjugate duality to establish existence of optimal portfolios in an assetallocation problem, with the goal of minimizing the variance of the final wealth which results from trading over a fixed finite horizon in a continuoustime complete market, subject to the constraints that the expected final wealth equal a specified target value, and the portfolio of the investor, defined by the dollar amount invested in each stock, takes values in a given closed convex set. The asset prices are modelled by Ito ̂ processes, for which the market parameters are random processes adapted to the information filtration available to the investor. We synthesize a dual optimization problem and establish a set of optimality relations, similar to the EulerLagrange and transversality relations of calculus of variations, giving necessary and sufficient conditions for the given optimization problem and its dual to each have a solution, with zero duality gap. We then resolve these relations to establish existence of an optimal portfolio.
Asymptotic Behaviour of MeanQuantile Efficient Portfolios ∗
, 2005
"... In this paper we investigate portfolio optimization in a BlackScholes continuoustime setting under quantile based risk measures: value at risk, capital at risk and relative value at risk. We show that the optimization results are consistent with Merton’s TwoFund Separation Theorem, i.e., that ever ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In this paper we investigate portfolio optimization in a BlackScholes continuoustime setting under quantile based risk measures: value at risk, capital at risk and relative value at risk. We show that the optimization results are consistent with Merton’s TwoFund Separation Theorem, i.e., that every optimal strategy is a weighted average of the bond and Merton’s portfolio. We present optimization results obtained under constrained versions of the above risk measures, including the fact that under value at risk, in better markets and during longer time horizons, it is optimal to invest less into the risky assets. 1