arXiv subjects

Mario Sikic

Publications and source records attributed to Mario Sikic.

5 recordsLinked to original sources

arXiv2019

Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of problems covered by our robust optimization problem includes optimal stopping and semi-static trading under Knightian uncertainty.

math.OC↗

arXiv2018

Robust martingale selection problem and its connections to the no-arbitrage theory

We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in examples spanning frictionless markets, models with proportional transaction costs and also models for illiquid markets. In all these examples, we also incorporate trading constraints.

q-fin.MF↗

arXiv2018

Robust Utility Maximization in Discrete-Time Markets with Friction

We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of an utility maximizer in the frictionless market model, markets with proportional transaction costs and also more general convex costs, like in the case of market impact.

q-fin.MF↗

arXiv2016

Diversification, protection of liability holders and regulatory arbitrage

Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider surplus-invariant capital adequacy tests, i.e. tests that do not depend on the surplus of a financial institution. We provide a complete characterization of closed, convex, surplus-invariant capital adequacy tests that highlights an inherent tension between surplus-invariance and the desire to give credit for diversification. The second objective leads to requiring consistency of capital adequacy tests across jurisdictions. Of particular importance in this respect are capital adequacy tests that remain invariant under a change of numéraire. We establish an intimate link between surplus- and numéraire invariant tests.

q-fin.RM↗

arXiv2015

Financial market models in discrete time beyond the concave case

In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables describing the outcome of trading. We do not make any concavity assumptions. The first result is that under sequential upper-semicontinuity the market model can be represented as a normal integrand. We then extend the concept of no-arbitrage to this setup and study its consequences as the super-hedging theorem and utility maximization. Finally, we show how to extend the concepts and results to the case of vector-valued market models, an example of which is the Kabanov model of currency markets.

q-fin.MF↗