A note on super-hedging for investor–producers

We study the situation of an agent who can trade on a financial market and can also transform some assets into others by means of a production system, in order to price and hedge derivatives on produced goods. This framework is motivated by the case of an electricity producer who wants to hedge a position on the electricity spot price and can trade commodities which are inputs for his system. This extends the essential results of Bouchard and Nguyen (Math Finance, 2011) to continuous time markets. We introduce the generic concept of conditional sure profit along the idea of the no sure profit condition of Rásonyi (Optimality and risk-modern trends in mathematical finance: the Kabanov Fetschrift, 2009). The condition allows one to provide a closedness property for the set of super-hedgeable claims in a very general financial setting. Using standard separation arguments, we then deduce a dual characterization of the latter and provide an application to power futures pricing.     

A note on the Fuglede–Putnam theorem

We prove the following generalization of the Fuglede–Puntam theorem. Let N be an unbounded normal operator in the Hilbert space, and let A be an unbounded self-adjoint operator such that $D(N)\subseteq D(A)$ . Then, $ AN\subseteq N^*A \Rightarrow AN^*\subseteq NA.$      

A note on K?hler–Ricci flow

Let g(t) with ${t\in [0,T)}$ be a complete solution to the K?hler–Ricci flow: ${\frac{d}{dt}g_{i\bar j}=-R_{i\bar j}}$ where T may be ∞. In this article, we show that the curvature of g(t) is uniformly bounded if the solution g(t) is uniformly equivalent. This result is stronger than the main result in ?e?um (Am J Math 127(6):1315–1324, 2005) within the category of K?hler–Ricci flow.     

A note on Robinson–Ursescu and Lyusternik–Graves theorem

The aim of this note is twofold. First, we prove an analogue of the well-known Robinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linear mapping is restricted to a closed convex subset of a Banach space.     

A note on θ-tightness

In questo lavoro chiariamo il ruolo che la θ-tightness (introdotta dagli autori in [2]) ha nel determinare alcune estensioni di sottoinsiemi di uno spazio topologico.     

A note on Marino-Vafa formula

Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes.     

A note on β-connectedness

An example is given to show that there exists a generalized topological space which is irreducible but not β-connected. This gives an answer to Question 2.8 in [6]. Besides, some characterizations of β-connectedness are obtained.     

A note on asymptotic pointwise weaker Meir–Keeler-type contractions

In this work, we first define the asymptotic pointwise weaker Meir–Keeler-type $\psi$-contraction, $\psi :X\to {?}^{+}$, and then a simple proof for the existence of fixed point theorems for the asymptotic pointwise weaker Meir–Keeler-type $\psi$-contraction is given.     

A note on Weil index

Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(?))γ(1,(?))(a,b)andγ(a,(?))~4 =(-1,-1),where(a,b)is the Hilbert symbol for F.The Weil index plays an important role in the theory of theta series and in the general representation theory.In this paper,we establish an identity relating the Weil indexγ(a,(?))and the Gauss sum.     

A note on the Moll–Arias de Reyna integral

The Ramanujan Journal - The Moll–Arias de Reyna integral $$\begin{aligned} \int _0^{\infty }\frac{\mathrm{d}x}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi (x)+\sqrt{\varphi (x)}}} \quad \text {...     

A note on a nonlocal nonlinear reaction–diffusion model

We give an application of the Crandall–Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.     

A note on Liu–Iwamura’s dependent-chance programming

Sometimes a complex stochastic decision system undertakes multiple tasks called events, and the decision-maker wishes to maximize the chance functions which are defined as the probabilities of satisfying these events. Originally introduced by Liu and Iwamura [B. Liu, K. Iwamura, Modelling stochastic decision systems using dependent-chance programming, European Journal of Operational Research 101 (1997) 193–203], dependent-chance programming is aimed at maximizing some chance functions of events in an uncertain environment. In this work, we show that the original dependent chance-programming framework needs to be extended in order to capture an exact reliability measure for a given plan.     

A note on asymptotic behaviour of Mittag–Leffler functions

In this paper, we give a short note on the asymptotic behaviour of the two parameter Mittag–Leffler function. Useful results are collected for the reader and also explicit estimation formulas for this function are obtained which will play a role in existence and stability theory of fractional differential equations.     

A note on nonnegative Bakry–Émery Ricci curvature

In this note, we show that if M ⁿ is a nonnegatively Bakry–émery-Ricci curved manifold with bounded potential function, any finitely generated subgroup of the fundamental group of M has polynomial growth of degree less than or equal to n.     

A note on monotone mean–variance preferences for continuous processes

We extend a recent result of Trybuła and Zawisza (2019), who investigate a continuous-time portfolio optimization problem under monotone mean–variance preferences. Their main finding is that the optimal strategies for monotone and classical mean–variance preferences coincide in a stochastic factor model for the financial market. We generalize this result to any model for the financial market where asset prices are continuous.