Related papers: Multistage Portfolio Optimization: A Duality Resul…
We use the martingale method to discuss the relationship between mean-variance (MV) and monotone mean-variance (MMV) portfolio selections. We propose a unified framework to discuss the relationship in general financial markets without any…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets…
We introduce a generic solver for dynamic portfolio allocation problems when the market exhibits return predictability, price impact and partial observability. We assume that the price modeling can be encoded into a linear state-space and…
In this paper we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality…
We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage…
We give an algebraic definition of a Markowitz market and classify markets up to isomorphism. Given this classification, the theory of portfolio optimization in Markowitz markets without short selling constraints becomes trivial.…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of [Kabanov, Y., Hedging and…
We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically…
The idiosyncratic (microscopic) and systemic (macroscopic) components of market structure have been shown to be responsible for the departure of the optimal mean-variance allocation from the heuristic `equally-weighted' portfolio. In this…
In the portfolio multiobjective optimization framework, we propose to compare and choose, among all feasible asset portfolios of a given market, the one that maximizes the product of the distances between its values of risk and gain and…
We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud…
This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in 1976. We derive an explicit dual problem in terms of two dual variables, one of which is the…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the…
We investigate the optimal estimation of a quantum process that can possibly consist of multiple time steps. The estimation is implemented by a quantum network that interacts with the process by sending an input and processing the output at…
This paper studies the static economic optimization problem of a system with a single aggregator and multiple prosumers in a Real-Time Balancing Market (RTBM). The aggregator, as the agent responsible for portfolio balancing, needs to…