Some reflections on past and future of nonlinear dynamics in economics and finance

This paper offers an overview of the literature on the economic and financial applications of theory of nonlinear dynamics, especially bifurcation theory. After a short introductory discussion of the first nonlinear dynamic models in social sciences and the economic relevance of the zoo of bifurcations and complicated dynamics that such models can generate, we present an overview of the literature on nonlinear dynamic models in the areas of underdevelopment, environmental poverty traps, the management of common goods, industrial organization and financial markets. The review of the literature is enriched by reflections and ideas for future research.     

Reference group influence on binary choices dynamics

The recent literature has analyzed binary choices dynamics providing interesting results. Most of these contributions consider interactions within a single group. Nevertheless, in some situations the interaction takes place not only within a single group but also between different groups. In this paper, we investigate the choice dynamics when considering two populations where one serves as a reference group. Considering this influence effect enriches the dynamics. Although the structurally stable resulting dynamics are attracting cycles only, with any positive integer period, the reference group makes the dynamics of the influenced population much more complex. We considered both the possibility that the reference group has the same or the opposite attitude toward the distribution over the choices. We show how the dynamics and the bifurcation structure are modified under the influence of the reference group. Our results illustrate how the propensity to switch choices in the reference groups may, indirectly, affect choices in the first group.     

A model of growth with inherited tastes

This research aims at studying a general equilibrium closed economy with overlapping generations and inherited tastes (aspirations), as in de la Croix (Econ Lett 53(1):89–96, 1996). It shows that the interaction between the intensity of aspirations and the elasticity of substitution of effective consumption affects the qualitative and quantitative long-term dynamics from both local and global perspectives. The related literature is extended by showing that (1) the Neimark–Sacker bifurcation found by de la Croix (1996) does not necessarily give rise to fluctuations and (2) endogenous (long-lasting) fluctuations occur through the emergence of period-doubling bifurcations.     

Optimal strategy for a fund manager with option compensation

I consider the problem of portfolio optimization for a manager whose compensation is given by the sum of a constant and a variable term. The constant term is a fixed percentage of the managed funds that is payed to the manager independently of his performance. The variable term is a premium that is proportional to the profit earned by the manager over a benchmark at a certain evaluation date. I find the optimal strategy and the optimal portfolio value in the Black–Scholes setting when the benchmark is a linear combination of the risky asset and the money market account.     

“Speculative Influence Network” during financial bubbles: application to Chinese stock markets

We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion and a bubble regime represented by the stochastic super-exponential Sornette and Andersen (Int J Mod Phys C 13(2):171–188, 2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the bubble regime, we then use the transfer entropy to quantify the influence of the returns of one asset i onto another asset j, from which we introduce the adjacency matrix of the SIN among securities. We apply our technology to the Chinese stock market during the period 2005–2008, during which a normal phase was followed by a spectacular bubble ending in a massive correction. We introduce the Net Speculative Influence Intensity variable as the difference between the transfer entropies from i to j and from j to i, which is used in a series of rank ordered regressions to predict the maximum loss (%MaxLoss) endured during the crash. The sectors that influenced other sectors the most are found to have the largest losses. There is some predictability obtained by using the transfer entropy involving industrial sectors to explain the %MaxLoss of financial institutions but not vice versa. We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may contribute significant skill to the development of general linkage-based systemic risks measures and early warning metrics.     

Obtaining collaboration benefits: the role of collaboration-specific investment and absorptive capacity in China

This study examines the role of collaboration-specific investment and absorptive capacity on the attainment of interorganizational collaboration benefits. Grounded in the extended resource-based view, and using survey data from Chinese executives, we study the driver for, and test the impacts of, collaboration-specific investment and organizational learning on collaboration performance. Our findings indicate that resource similarity between the collaborative partners affects the level of collaboration-specific investment and learning, and demonstrate an approach that firms can use to obtain both abnormal common and private benefits from participation in an interorganizational collaboration. Specifically, the findings suggest that collaboration-specific investment has a direct effect on the enhancement of absorptive capacity and attainment of common and private collaboration benefits. Furthermore, due to the direct effect of absorptive capacity on attainment of collaboration benefits, commitment of collaboration-specific investment has an indirect effect on the attainment of common and private collaboration benefits. This study is the first to apply both the competence-capability framework and extended resource-based view to study interorganizational collaboration. In fact, this study aims to determine mechanisms for a collaboration-participating firm to obtain more benefit, whether common or private. Our findings provide support for the importance of learning capability as a factor in the acquisition of collaboration benefits.     

Does a central clearing counterparty reduce liquidity needs?

This study investigates whether and how central clearing influences the overall liquidity needs in a network of financial obligations. Utilizing the approach of flow network theory, we show that the effect of adding a central clearing counterparty (CCP) is decomposed into two effects: central routing, and central netting effects. Each effect can produce different liquidity needs according to different liquidity scenarios. The analysis indicates that adding a CCP in times of financial distress successfully reduces the overall liquidity needs if and only if the netting efficiency of the CCP is sufficiently high. Furthermore, once the economy is no longer in financial distress, higher netting efficiency of the CCP could conversely increase the overall liquidity needs. The results have implications for the effectiveness of CCPs in mitigating systemic risk in times of financial distress, and their operating costs once the distress has passed.     

Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring

In this paper, a structural analysis of hybrid censoring models is presented. This new modularization approach to hybrid censoring models enables a convenient derivation of distributional results. For instance, it allows to derive the exact distribution of the MLEs under an exponential assumption for very complex hybrid scenarios. In order to illustrate the benefit of this idea, we apply it to four new unified progressive hybrid censoring schemes. They are extensions of already proposed unified Type-I/II/III/IV hybrid censoring schemes to progressively Type-II censored data. The resulting analysis shows that the modularization approach provides a powerful, efficient, and elegant tool to study even more complex hybrid censoring models.