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In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following…
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic…
In this paper, we provide a representation theorem for dynamic capital allocation under It{\^o}-L{\'e}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with…
In this paper we investigate the applicability of a recently introduced primal-dual splitting method in the context of solving portfolio optimization problems which assume the minimization of risk measures associated to different convex…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
This paper is devoted to proposing a new asymmetric risk-sensitive criterion involving different risk attitudes toward varying risk sources. The criterion can only be defined through the initial value of the minimal solutions of quadratic…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth $X^*(T) : = X_{\varphi^*}(T)$ of the problem to maximize the expected $U$-utility…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
In this paper, we study the robust optimal investment and risk control problem for an insurer who owns the insider information about the financial market and the insurance market under model uncertainty. Both financial risky asset process…
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…
We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected…
Convex risk measures play a foundational role in the area of stochastic optimization. However, in contrast to risk neutral models, their applications are still limited due to the lack of efficient solution methods. In particular, the mean…
The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…