Asset Pricing With No Exogenous Probability Measure

Abstract

Abstract. In this paper we propose a model of …nancial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite …nite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on …nitely additive measures. From this representation we derive an exact decomposition of the rsik premiu as the sum of the correlation of returns with the market price of risk and an additional term, the purely …nitely additive premium, related to the jumps of the return process. We also discuss the implications of the absence of free lunches.

Robust pricing–hedging dualities in continuous time

“…On a philosophical level, we start with the "universally acceptable" setting and proceed by ruling out more and more scenarios as impossible; see also Cassese [15]. We may proceed in this way until we end up with paths supporting a unique martingale measure, e.g.…”

Asset pricing in an imperfect world

“…In his pioneering work, de Finetti [13] introduced the idea of modeling the qualitative judgment "event A is more likely than B" as a binary relation, A B It is easily seen that, adding the axiom (e) ∅ Ω, then dF is a regular stochastic order exactly because the collection {A ⊂ Ω : A ∅} is an ideal of subsets of Ω. A generalization of this idea was introduced in [8] where an ideal N of so-called negligible events (not including Ω) was taken as a primitive and a corresponding order N was defined as in (9), i.e.…”

“…Of course, the supremum of a family of integrals may be represented as the Choquet integral with respect to a supermodular capacity having M as its core 8 . Differently from classical asset pricing formulas, the fundamental value is not linear here, due to transaction costs.…”

Complete and Competitive Financial Markets in a Complex World

“…In addition to market power, our model departs from traditional financial literature inasmuch as it lacks of any particular mathematical structure, topological or measure theoretic. In particular, following the thread of our previous papers [10] and [13], we do not assume the existence of any exogenously given probability measure. Although this choice implies giving up the powerful artillery of stochastic analysis, particularly in continuous time, it permits, we believe, a better understanding of how financial markets work in a context of unrestricted complexity.…”

“…Although this choice implies giving up the powerful artillery of stochastic analysis, particularly in continuous time, it permits, we believe, a better understanding of how financial markets work in a context of unrestricted complexity. A thorough discussion of the reasons supporting this choice may be found in [10].…”