arXiv subjects

Keita Owari

Publications and source records attributed to Keita Owari.

7 recordsLinked to original sources

arXiv2024

Semistatic robust utility indifference valuation and robust integral functionals

We consider a discrete-time robust utility maximisation with semistatic strategies, and the associated indifference prices of exotic options. For this purpose, we introduce a robust form of convex integral functionals on the space of bounded continuous functions on a Polish space, and establish some key regularity and representation results, in the spirit of the classical Rockafellar theorem, in terms of the duality formed with the space of Borel measures. These results (together with the standard Fenchel duality and minimax theorems) yield a duality for the robust utility maximisation problem as well as a representation of associated indifference prices, where the presence of static positions in the primal problem appears in the dual problem as a marginal constraint on the martingale measures. Consequently, the resulting indifference prices are consistent with the observed prices of vanilla options.

math.FA↗

arXiv2018

Convex functions on dual Orlicz spaces

In the dual $L_{Φ^*}$ of a $Δ_2$-Orlicz space $L_Φ$, that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology $τ(L_{Φ^*},L_Φ)$ if and only if on each order interval $[-ζ,ζ]=\{ξ: -ζ\leq ξ\leqζ\}$ ($ζ\in L_{Φ^*}$), it is lower semicontinuous (resp. continuous) for the topology of convergence in probability. For this purpose, we provide the following Komlós type result: every norm bounded sequence $(ξ_n)_n$ in $L_{Φ^*}$ admits a sequence of forward convex combinations $\barξ_n\in\mathrm{conv}(ξ_n,ξ_{n+1},...)$ such that $\sup_n|\barξ_n|\in L_{Φ^*}$ and $\barξ_n$ converges a.s.

math.FA↗

arXiv2015

A Robust Version of Convex Integral Functionals

We study the pointwise supremum of convex integral functionals $\mathcal{I}_{f,γ}(ξ)= \sup_{Q} \left( \int_Ωf(ω,ξ(ω))Q(dω)-γ(Q)\right)$ on $L^\infty(Ω,\mathcal{F},\mathbb{P})$ where $f:Ω\times\mathbb{R}\rightarrow\overline{\mathbb{R}}$ is a proper normal convex integrand, $γ$ is a proper convex function on the set of probability measures absolutely continuous w.r.t. $\mathbb{P}$, and the supremum is taken over all such measures. We give a pair of upper and lower bounds for the conjugate of $\mathcal{I}_{f,γ}$ as direct sums of a common regular part and respective singular parts; they coincide when $\mathrm{dom}(γ)=\{\mathbb{P}\}$ as Rockafellar's result, while both inequalities can generally be strict. We then investigate when the conjugate eliminates the singular measures, which a fortiori yields the equality in bounds, and its relation to other finer regularity properties of the original functional and of the conjugate.

math.FA↗

arXiv2014

Maximum Lebesgue Extension of Monotone Convex Functions

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit construction, where the maximum domain of extension is obtained as a (possibly proper) subspace of a natural Orlicz-type space, characterized by a certain uniform integrability property. As an application, we provide a characterization of the Lebesgue property of monotone convex function on arbitrary solid spaces of random variables in terms of uniform integrability and a "nice" dual representation of the function.

math.FA↗

arXiv2013

On the Lebesgue Property of Monotone Convex Functions

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual representation by order-continuous linear functionals. This generalizes and unifies several recent results obtained in the context of convex risk measures.

math.FA↗

arXiv2012

On Admissible Strategies in Robust Utility Maximization

The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a "good definition" of admissible strategies, so that an optimizer is obtained. Under suitable assumptions, especially a time-consistency property of the set of probabilities which describes the model uncertainty, we show that an optimal strategy is obtained in the class of strategies whose wealths are supermartingales under all local martingale measures having a finite generalized entropy with at least one of candidate models (probabilities).

q-fin.PM↗

arXiv2011

Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endowment. To obtain this duality, we prove a robust version of Rockafellar's theorem on convex integral functionals and apply Fenchel's general duality theorem.

q-fin.CP↗