Related papers: Free Lunch
Stemming from a paper of Auger and Teytaud, there is a common misconception that for continuous domains No Free Lunch (NFL) does not hold. However, Rowe, Vose, and Wright have demonstrated that NFL holds for arbitrary domains and…
This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and…
In normal times, it is assumed that financial institutions operating in non-overlapping sectors have complementary and distinct outcomes, typically reflected in mostly uncorrelated outcomes and asset returns. Such is the reasoning behind…
This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing…
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
Token economics has emerged as a useful lens for understanding resource allocation, value creation, and pricing in large language model systems. While recent work has increasingly treated tokens as economic primitives, there remains a…
We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a model-independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
The No Free Lunch (NFL) theorem guarantees equal average performance only under uniform sampling of a function space closed under permutation (c.u.p.). We ask when this averaging ceases to reflect what benchmarking actually reports. We…
This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain…
We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no-arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs.…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
In his stimulating article on the reasons for two puzzling observations about the behaviour of interest rates, exchange rates and the rate of inflation, Charles Engel (2016) puts forward an explanation that rests on the concept of a…
We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there…
Experimental results on market behavior establish a lower stability and efficiency of markets for durable re-tradable assets compared to markets for non-durable, or perishable, goods. In this chapter, we revisit this known but…
We study the concept of financial bubble in a market model endowed with a set of probability measures, typically mutually singular to each other. In this setting we introduce the notions of robust bubble and robust fundamental value in a…
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We…
Quantum computers have the potential to provide an advantage for financial pricing problems by the use of quantum estimation. In a broader context, it is reasonable to ask about situations where the market and the assets traded on the…
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…