Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1511.00468

Real Options and Threshold Strategies

Vadim Arkin·Alexander Slastnikov
View original source ↗Read source document ↗Export metadata ↓

Abstract

The paper considers an investment timing problem appearing in real options theory. Present values from an investment project are modeled by general diffusion process. We prove necessary and sufficient conditions under which an optimal investment time is induced by threshold strategy. We study also the conditions of optimality of threshold strategy (over all threshold strategies) and discuss the connection between solutions to investment timing problem and to free-boundary problem.

Explore related subjects

q-fin.MFmath.PRq-fin.PM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vadim Arkin, Alexander Slastnikov. 2015-11-02. Real Options and Threshold Strategies. https://arxiv.org/abs/1511.00468

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Affine Pricing Models from Group Quantization and Holonomy

The analytic tractability of affine pricing models is usually expressed through two complementary formulations: a coordinate-space pricing operator and an exponential-affine transform representation governed by generalized Riccati equations. We develop \emph{Affine Holonomy Group Quantization} (AHGQ) as a geometric framework in which these two formulations arise from the same underlying structure. The construction separates the affine pricing symbol into a homogeneous quadratic sector and a complementary affine sector. The first generates a finite-dimensional symplectic transport and a centrally extended Lie group, while the second is represented by a multiplicative holonomy carried by a thin-path groupoid. Their combination determines an affine Poincaré--Cartan form. Its characteristic dynamics reduce in momentum variables to the generalized Riccati system and its scalar amplitude, whereas the coordinate representation recovers the standard affine pricing operator. Representative Gaussian and square-root models illustrate the construction. The contribution is structural: AHGQ gives a common geometric origin to the coordinate and transform representations of continuous-path, time-homogeneous affine pricing models.

q-fin.MF↗
arXiv2026

Asset price bubbles under model uncertainty and short-sale constraints: A discrete-time analysis

In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short-sale constraints. Using a super-hedging valuation benchmark, we study the difference between the asset's market price and its fundamental value in this constrained market. We examine how assumptions on the liquidation time affect the conditional expectation bounds satisfied by the resulting bubble process. For assets with bounded maturity and no dividend payments, the G-supermartingale property of prices provides a necessary and sufficient condition for the existence of bubbles. In contrast, when maturity is unbounded, the infi-supermartingale property yields a necessary condition, while the G-supermartingale property remains sufficient. We also show that no dominance rules out bubbles when the liquidation time is bounded. For finite-horizon contingent claims, we distinguish upper-valuation relations from no-dominance benchmarks. Fundamental prices satisfy put-call bounds, whereas market prices satisfy put-call parity under no dominance. In the dividend-free setting, the same assumptions imply equality between American and European call fundamental values and, under the stated trading conditions, between their market prices.

q-fin.MF↗
arXiv2026

Optimal investment under capital gains taxes

We generalize classical existence results for expected utility maximization 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 negative taxes but can only be offset against potential gains in the future. Central to the analysis is a well-known phenomenon from arbitrage-free markets with proportional transaction costs that does not exist in arbitrage-free frictionless markets: an investment in specific quantities of stocks that is completely riskless but may provide an advantage over holding money in the bank account. As a result of this phenomenon, on an infinite probability space, no-arbitrage does not imply that the set of attainable terminal wealth is closed in probability. We provide simple sufficient conditions for closedness. Then, we characterize the closure of the set of attainable terminal wealth, thereby identifying precisely the source of non-closedness. As a by-product, we obtain a new construction for an integrable majorant that dominates the utilities of all nonnegative terminal wealth attainable from a given initial capital in a frictionless market and that works directly in multiperiod models.

q-fin.MF↗