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The constructive approach to mathematics has the advantage that witnesses can be extracted from statements of existence and theorems can be unwound to give algorithms. Even better, constructive theorems can be interpreted in any topos,…
An arbitrage strategy allows a financial agent to make certain profit out of nothing, i.e., out of zero initial investment. This has to be disallowed on economic basis if the market is in equilibrium state, as opportunities for riskless…
This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage…
In this paper we study the concept of algebraic core for convex sets in general vector spaces without any topological structure and then present its applications to problems of convex analysis and optimization. Deriving the equivalence…
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties…
We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with…
Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of…
Although the valuation of life contingent assets has been thoroughly investigated under the framework of mathematical statistics, little financial economics research pays attention to the pricing of these assets in a non-arbitrage, complete…
Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we…
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a…
We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are…
We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov and al. (2002), Kabanov and…
We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not…
In the paper we study markets with concave transaction costs which depend in a concave way on the volume of transaction. This is typical situation in the case of small investors, which commonly appears in currency and real estate markets.…
In this paper we report further progress towards a complete theory of state-independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions we establish a…
We introduce the concept of numeraires of convex sets in the nonnegative orthant of the topological vector space of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set to…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…