Abstract We analyze historical data of stock-market prices for multiple financial indices using the concept delay-time averaging time series (FTS). The region validity our recent theoretical predictions [Cherstvy A G et al 2017 New J. Phys. 19 063045] standard and delayed time-averaged mean-squared ‘displacements’ (TAMSDs) FTS is extended to all lag times. As first novel element, we perform ext...

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [7] that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion ...

We propose a novel estimator for the amount of international risk sharing that depends exclusively on asset returns data. In particular, our estimator has a nonparametric flavor in that it makes no parametric assumption on preferences and on the stochastic process that governs the dynamics of asset returns. This is in contrast with the existing estimators in the literature that either assume a ...

For decades financial economists have been attempted to determine the optimal investment policy by recognizing the option value embedded in irreversible investment whose project value evolves as a geometric Brownian motion (GBM). This paper aims to examine the effects of the optimal investment trigger and of the misspecification of stochastic processes on investment in real options applications...

2) and 3) together can be summarized by: If t0 = 0 < t1 < t2 < · · · < tk, then the increment rvs B(ti) − B(ti−1), i ∈ {1, . . . k}, are independent with B(ti) − B(ti−1) ∼ N(0, ti − ti−1) (normal with mean 0 and variance ti − ti−1). In particular, B(ti) − B(ti−1) is independent of B(ti−1) = B(ti−1)−B(0). If we only wish to simulate B(t) at one fixed value t, then we need only generate a unit no...

In the valuation of forest resources, alternative use land is one central themes. most cases it made without taking into account uncertainty and possible flexibility use. Within these alternatives, strategy shifting to a more profitable sustainable crop well-studied topic in research. Although transformation opportunity could add great value project, this obviated by traditional discounted cash...

We consider a popular problem in finance, option pricing, through the lens of an online learning game between Nature and an Investor. In the Black-Scholes option pricing model from 1973, the Investor can continuously hedge the risk of an option by trading the underlying asset, assuming that the asset’s price fluctuates according to Geometric Brownian Motion (GBM). We consider a worst-case model...