In this review paper we summarise several nonparametric methods recently applied to the pricing of financial options. After a short introduction to martingale-based option pricing theory, we focus on two possible fields of application for nonparametric methods: the estimation of risk-neutral probabilities and the estimation of the dynamics of the underlying instruments in order to construct an ...

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in thi...

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with t...

This paper analyzes four kinds of Cantonese polar questions, HO2, ME1, AA4 and A-NOTA questions in the framework of radical inquisitive semantics (Groenendijk & Roelofsen, 2010; Aher, 2012; Sano, 2014). HO2, ME1 and A-NOT-A questions have multidimensional semantics. In addition to their primary speech act of questioning, HO2 and ME1 interrogatives encode secondary assertive acts of positive and...

The present note addresses an open question concerning a sufficient characterization of the variance-optimal martingale measure. Denote by S the discounted price process of an asset and suppose that Q? is an equivalent martingale measure whose density is a multiple of 1− φ • ST for some S-integrable process φ. We show that Q? does not necessarily coincide with the variance-optimal martingale me...

For any discrete-time P–local martingale S there exists a probability measure Q ∼ P such that S is a Q–martingale. A new proof for this result is provided. This proof also yields that, for any ε > 0, the measure Q can be chosen so that dQ/dP ≤ 1 + ε.

In this paper we treat, under fairly general conditions, the question of whether asset prices admit a martingale measure when the markets are free of arbitrage opportunities. The arbitrage opportunities we consider are restricted to originate from simple trading strategies, which are most closely related to actual market portfolios. It is shown that if such simple arbitrage profits are excluded...

We discuss the sensitivity of the high-scale supersymmetry (SUSY) at 10–1000 TeV in B, Bs, K and D meson systems together with the neutron electric dipole moment (EDM) and the mercury EDM. In order to estimate the contribution of the squark flavor mixing to these flavor changing neutral currents (FCNCs), we calculate the squark mass spectrum, which is consistent with the recent Higgs discovery....

We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).

We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modelled by a suitably integrable, strictly positive, càdlàg process S over [0, T ]. Every option price is defined as the conditional expectation under a given equivalent (true) martingale measure P, the same for all options. We show that every positive contingent claim on S can be ...