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In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model, by using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction term, we use Mellin transform. We also conduct a sensitivity analysis on these formulas, and compare the option prices calculated by them with those generated by Monte-Carlo simulation., Comment: 19 pages with 4 figures

In this paper, we introduce the concept of $\Delta$-convexity in an abstract economy with all choice sets being general topological spaces. We give a new generalization of the classical Yannelis-Prabhakar equilibrium existence theorem in abstract economies by relaxing $SS$-convexity to $\Delta$-convexity., Comment: 9 pages

A quasi-continuous dynamical system is a pair $(X,f)$ consisting of a topological space $X$ and a mapping $f: X\to X$ such that $f^n$ is quasi-continuous for all $n \in \mathbb N$, where $\mathbb N$ is the set of non-negative integers. In this paper, we show that under appropriate assumptions, various definitions of the concept of topological transitivity are equivalent in a quasi-continuous dynamical system. Our main results establish the equivalence of topological and point transitivity in a quasi-continuous dynamical system. These extend some classical results on continuous dynamical systems in [3], [10] and [25], and some results on quasi-continuous dynamical systems in [7] and [8]., Comment: 14

This paper investigates the ex-post core and its relationships to the fine core and the set of rational expectations equilibrium allocations in an oligopolistic economy with asymmetric information, in which the set of agents consists of some large agents and a continuum of small agents and the space of states of nature is a general probability space. We show that under appropriate assumptions, the ex-post core is not empty and contains the set of rational expectations equilibrium allocations. We provide an example of a pure exchange continuum economy with asymmetric information and infinitely many states of nature, in which the ex-post core does not coincide with the set of rational expectations equilibrium allocations. We also show that when our economic model contains either no large agents or at least two large agents with the same characteristics, the fine core is contained in the ex-post core., Comment: 23 pages

In this paper, we continue to study pairwise ($k$-semi-)stratifiable bitopological spaces. Some new characterizations of pairwise $k$-semi-stratifiable bitopological spaces are provided. Relationships between pairwise stratifiable and pairwise $k$-semi-stratifiable bitopological spaces are further investigated, and an open question recently posed by Li and Lin in \cite{LL} is completely solved. We also study the quasi-pseudo-metrizability of a topological ordered space $(X, \tau, \preccurlyeq)$. It is shown that if $(X, \tau, \preccurlyeq)$ is a ball transitive topological ordered $C$- and $I$-space such that $\tau$ is metrizable, then its associated bitopological space $(X,\tau^{\flat},\tau^{\natural})$ is quasi-pseudo-metrizable. This result provides a partial affirmative answer to a problem in \cite{KM}., Comment: 13 pages

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possess the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirmed that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.

Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and other hyperspace topologies, and applications of the Wijsman topology in analysis have been explored. However, there are still several fundamental open problems on this topology. In this article, the author gives a brief survey on these problems and some up-to-date partial solutions., Comment: 9 pages

In previous work by Beer and Levi [8, 9], the authors studied the oscillation $\Omega (f,A)$ of a function $f$ between metric spaces $\langle X,d \rangle$ and $\langle Y,\rho \rangle$ at a nonempty subset $A$ of $X$, defined so that when $A =\{x\}$, we get $\Omega (f,\{x\}) = \omega (f,x)$, where $\omega (f,x)$ denotes the classical notion of oscillation of $f$ at the point $x \in X$. The main purpose of this article is to formulate a general joint continuity result for $(f,A) \mapsto \Omega (f,A)$ valid for continuous functions., Comment: 13 pages

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model parameters that switch according to a continuous-time observable Markov chain process. A semi-closed form pricing formula for variance swaps is derived. The pricing formula is assessed through numerical implementations, and the impact of including regime-switching on pricing variance swaps is also discussed., Comment: 16 pages, 2 figures

Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. For every $n\in\mathbb{N}$, let $F_{n}(X)$ (resp. $A_n(X)$) denote the subspace of $F(X)$ (resp. $A(X)$) that consists of words of reduced length at most $n$ with respect to the free basis $X$. In this paper, we discuss two weak forms of countability axioms in $F(X)$ or $A(X)$, namely the $csf$-countability and $snf$-countability. We provide some characterizations of the $csf$-countability and $snf$-countability of $F(X)$ and $A(X)$ for various classes of spaces $X$. In addition, we also study the $csf$-countability and $snf$-countability of $F_n(X)$ or $A_n(X)$, for $n=2, 3, 4$. Some results of Arhangel'ski\v\i\ in \cite{A1980} and Yamada in \cite{Y1998} are generalized. An affirmative answer to an open question posed by Li et al. in \cite{LLL} is provided.

In this paper, we continue the study of function spaces equipped with topologies of (strong) uniform convergence on bornologies initiated by Beer and Levi \cite{beer-levi:09}. In particular, we investigate some topological properties these function spaces defined by topological games. In addition, we also give further characterizations of metrizability and completeness properties of these function spaces., Comment: 15 pages

In this paper, we study normality and metrizability of Wijsman hyperspaces. We show that every hereditarily normal Wijsman hyperspace is metrizable. This provides a partially answer to a problem of Di Maio and Meccariello in 1998., Comment: 8 pages

In this paper, a general model of a pure exchange differential information economy is studied. In this economic model, the space of states of nature is a complete probability measure space, the space of agents is a measure space with a finite measure, and the commodity space is the Euclidean space. Under appropriate and standard assumptions on agents' characteristics, results on continuity and measurability of the aggregate preferred correspondence in the sense of Aumann in [4] are established. These results together with other techniques are then employed to prove the existence of a maximin rational expectations equilibrium (maximin REE) of the economic model., Comment: 14 pages

In this paper, we study asymmetric information economies consisting of both non-negligible and negligible agents and having ordered Banach spaces as their commodity spaces. In answering a question of Herv\'{e}s-Beloso and Moreno-Garc\'{i}a, we establish a characterization of Walrasian expectations allocations by the veto power of the grand coalition. It is also shown that when an economy contains only negligible agents a Vind's type theorem on the private core with the exact feasibility can be restored. This solves a problem of Pesce., Comment: 23 pages

In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finite numbers of agents and states of nature and whose commodity space is a Banach lattice. The first one deals with Aubin non-dominated allocations, and the other claims that an allocation is a Walrasian expectations allocation if and only if it is not privately dominated by the grand coalition, by considering perturbations of the original initial endowments in precise directions., Comment: 20 pages

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R., Comment: 6 pages

Recently, Mr\v{s}evi\'{c} and Reilly discussed some covering properties of a topological space and its associated $\alpha$-topology in both topological and bitopological ways. The main aim of this paper is to investigate some common and controversial covering properties of $\cal T$ and ${\cal T}^{\alpha}$., Comment: 11 pages