Related papers: Portfolio optimization with two quasiconvex risk m…
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust…
We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional…
The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the…
We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the…
We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston's stochastic volatility model. We apply the duality methods developed in previous work to…
This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…
We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk…
We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement…
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be…
We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions…
This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the portfolio from a known dual representation of expectile and…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost…
In the conditional setting we provide a complete duality between quasiconvex risk measures defined on $L^{0}$ modules of the $L^{p}$ type and the appropriate class of dual functions. This is based on a general result which extends the usual…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…