Narrow Results

In a numéraire-independent framework, we study a financial market with $N$ assets which are all treated in a symmetric way. We define the fundamental value ^∗S of an asset $S$ as its super-replication price and say that the market has a strong bubble if ^∗S and $S$ deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraire s for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.

Viability theory can be applied for determining viable capture basin for control problem in presence of uncertainty. We first recall the concepts of viability theory which allow to develop numerical methods for computing viable capture basin for control problems and guaranteed control problems. Recent developments of option pricing in the framework of dynamical games with constraints lead to the formulation of guaranteed valuation in terms of guaranteed viable-capture basin of a dynamical game. As an application we show how the viability/capturability algorithm evaluates and manages portfolios. Regarding viability/capturability issues, stochastic control is a particular use of tychastic control. We replace the standard translation of uncertainty by stochastic control problem by tychastic ones and the concept of stochastic viability by the one of guaranteed viability kernel. Considering the Cox–Rubinstein model, we extend algorithms for hedging portfolios in the presence of transaction costs and dividends using recent developments on hybrid calculus.

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the controls regulating viable evolutions. For tychastic systems (parameterized systems where the parameters are tyches, disturbances, perturbations, etc.), the palicinesia of a tyche measure the worst norm over time of the velocities of the tyches. The palicinesia function is the largest palicinesia threshold c such that all evolutions with palicinesia smaller than or equal to c are viable. For dynamical games where one parameter is the control and the other one is a tyche (games against nature or robust control), we define the guaranteed inertia function associated with any initial state-control-tyche triple the best of the worst of the norms of the velocities of the controls and of the tyches and study their properties. Viability Characterizations and Hamilton-Jacobi equations of which these inertia and palicinesia functions are solutions are provided.

Primary agricultural cooperative societies (PACSs) are the bases of cooperative credit structure in India. The cooperative credit structure functioning in Maharashtra state has three tiers. The main function of the PACSs is to provide short- and medium-term credit to its members. PACSs play a vital role in the socio-economic development of its members. Finance is the key to all types of activities. The efficient management of any society depends on the efficient management of finance. PACSs being financial intermediaries provide financial service with the objective of growth and profit. In the era of globalisation, PACSs face a different type of challenge which raises questions about the viability and sustainability of PACSs. A low resource base has been a major constraint in the effective functioning of PACSs. Financial stability has a direct bearing on the deposit mobilisation and overdue reduction. Limited resources result in low business activity. Limited resources, an increase in nonperforming asset, low recovery, overdue, lack of finance and lack of diversification have affected the viability of primary agricultural societies. Besides providing agriculture credit, some PACSs in Pune District are engaged in diversified activities. The PACSs that have diversified their business are more viable and sustain better than non-diversified societies. This chapter reports the viability analysis of selected PACSs in the Pune District. Multi-stage sampling technique was used. The primary and secondary data were mixed together. Primary data were collected with the help of specially designed schedules by conducting interviews, and secondary data were collected from different published sources and annual reports of PACSs. The study concludes that, as a result of the diversification, Talegoan Dhamdhere PACS in Shirur Block is potentially viable as compared to the Bhairawnath Kasarsai PACS in Mulshi Block of Pune District.