### Working Paper Series Cone-Constrained Continuous-Time Markowitz Problems Cone-Constrained Continuous-Time Markowitz Problems

"... Abstract The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and timedependent) closed cone. We first prove existence of a solution for convex constraints by showing that the space of constrained terminal gains, which is a space of stochastic integrals, is closed in L 2 . Then we use stochastic control methods to describe the local structure of the optimal strategy, as follows. The value process of a naturally associated constrained linear-quadratic optimal control problem is decomposed into a sum with two opportunity processes L ± appearing as coefficients. The martingale optimality principle translates into a drift condition for the semimartingale characteristics of L ± or equivalently into a coupled system of backward stochastic differential equations for L ± . We show how this can be used to both characterise and construct optimal strategies. Our results explain and generalise all the results available in the literature so far. Moreover, we even obtain new sharp results in the unconstrained case.

### Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

"... We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficie ..."

Abstract
- Add to MetaCart

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

### Portfolio optimization when expected stock

, 906

"... returns are determined by exposure to risk ..."

(Show Context)
### CONSTRAINED MARKETS: TIME CONSISTENCY IN EFFICIENCY AND MINIMUM-VARIANCE SIGNED SUPERMARTINGALE MEASURE

, 2014

"... ar ..."

### Research Article Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from bo ..."

Abstract
- Add to MetaCart

(Show Context)
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. 1.

### unknown title

"... Noname manuscript No. (will be inserted by the editor) Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria ..."

Abstract
- Add to MetaCart

(Show Context)
Noname manuscript No. (will be inserted by the editor) Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria