Optional decomposition and Lagrange multipliers

Let be the set of equivalent martingale measures for a given process , and let be a process which is a local supermartingale with respect to any measure in . The optional decomposition theorem for states that there exists a predictable integrand such that the difference is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.     

Taxation, agency conflicts, and the choice between callable and convertible debt

We analyze debt choice in light of taxes and moral hazard. The model features an infinite sequence of nonzero-sum stochastic differential games between equity and debt. Closed-form expressions are derived for all contingent-claims. If equity can increase volatility without reducing asset drift, callable bonds with call premia are optimal. Although callable bonds induce risk shifting, call premia precommit equity to less frequent restructuring and are tax-advantaged. Convertible bonds mitigate risk shifting, but only induce hedging if assets are far from the default threshold. Convertibles are optimal only if risk shifting reduces asset drift sufficiently.     

On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper

This note contains ramifications of results of Delbaen et al. (2002). Assuming that the price process is locally bounded and admits an equivalent local martingale measure with finite entropy, we show, without further assumption, that in the case of exponential utility the optimal portfolio process is a martingale with respect to each local martingale measure with finite entropy. Moreover, the optimal value always can be attained on a sequence of uniformly bounded portfolios.     

Resources of the firm, Russian high-technology startups, and firm growth

Russia possessed many world-class technologies prior to the break up of the Soviet Union. Entrepreneurial endeavors resulted from this technological ability as market forces encouraged individuals to leave the large state enterprises that produced those technologies. Founding characteristics of the firm impact the resources that are available to the startup firm. This study investigates the extent to which founding factors in Russia help high-technology firms to prosper. It was found that the team establishing the business mitigated the liability of newness. However, in contrast to the US, the culture of Russia does not produce negative results if the founding team grows very large. Additionally, it was shown that firms that pursued more technological products and enter the market later performed best.     

Narrative Transportation and Paratextual Features of Social Media in Viral Advertising

This study establishes that the experience of narrative transportation has a positive influence on viral advertising. The relative strength of this relationship, however, depends on several boundary conditions associated with the paratextual features of social networking service (SNS) environments. Specifically, it is stronger if the senders and intended receivers have personal ties. Moreover, the influence of narrative transportation is negatively moderated by advertising disclosure that elicits persuasion knowledge. Finally, the negative effect of persuasion knowledge is reduced if the ad appears with a higher number of “likes,” which increases social proof for viral ads. Implications regarding viral advertising and social media behaviors are discussed.     

A positive interest rate model with sticky barrier

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait for a random time until the rate is reinitialized to a (possibly random) strictly positive value. This setting ensures that all term rates are strictly positive.

Our objective is to provide a simple method to price zero-coupon bonds. A basic statistical study of the data at hand indeed suggests a switch to a different mode of behaviour when we get to a low level of interest rates. We introduce a variable for the time already spent at 0 (during the last stay) and derive the pricing equation for the bond. We then solve this partial integro-differential equation (PIDE) on its entire domain using a finite difference method (Cranck–Nicholson scheme), a method of characteristics and a fixed point algorithm. Resulting yield curves can exhibit many different shapes, including the S shape observed on the recent Japanese market.