Investments in R&D and Production Capacity with Uncertain Breakthrough Time:Private versus Social Incentives

The article considers a sequential investment project which starts with a product innovation phase, and subsequently, once R&D is completed, a production phase. The investment decision of the R&D phase involves choosing the time and the size of the R&D investment. The time to breakthrough is stochastic in which the instantaneous probability of innovation is increasing in the R&D investment size. Once R&D is completed the firm starts producing the new product. To do so, the firm first needs to invest in production capacity, the size of which must be determined. We compare the optimal investment decisions of the firm with those of the social planner and conclude that the firm invests too late in R&D and not enough in production capacity. We find that a proper subsidy policy, consisting of an R&D investment and a productive investment subsidy can make up for that. However, taking into account a budget constraint such that subsidy expenses cannot exceed the resulting increase in total surplus, learns that a first-best solution can only be reached if the demand situation is relatively stable, i.e., when growth and demand uncertainty are limited, or when the price elasticity of demand is low

On the Unification of Centralized and Decentralized Clearing Mechanisms in Financial Networks

We analyze clearing mechanisms in financial networks in which agents may have both monetary individual assets and mutual liabilities. A clearing mechanism prescribes mutual payments between agents to settle their mutual liabilities. The corresponding payments, summarized in a payment matrix, are made in accordance with agent specific claims rules that stem from the vast literature on claims problems. We show that large classes of centralized and decentralized clearing mechanisms all prescribe the same payment matrix under the condition that the underlying claims rules satisfy composition; a property satisfied by the proportional rule that is often applied in insolvency proceedings. This payment matrix is the one that contains the minimal amount of payments required to clear the network. In fact, we show that composition guarantees unification of clearing mechanisms in which agents pay simultaneously and clearing mechanisms in which agents pay sequentially in any arbitrary order. Therefore, for a given financial network, each clearing mechanism gives rise to the same transfer allocation. Moreover, we provide an axiomatic characterization of the corresponding mutual claims rule on the basis of five axioms: scale invariance, equal treatment of equals, composition, path independence and consistency. This characterization extends the analogous characterization for claims rules as given by Moulin (2000)

The Characterization of Clearing Payments in Financial Networks

Clearing payments are payments between agents to settle their mutual liabilities. The interdependence between agents in financial networks complicates the analysis of clearing payments as the extent to which an agent can pay its creditors depends not only on its own assets but also on the incoming payments from the other agents. Each financial network is endowed with agent-specific claims rules that prescribe how each agent pays its creditors. Consequently, our model not only captures standard principles of bankruptcy law, such as limited liability of equity, absolute priority of debt over equity, proportionality, and priority, but also allows for more general underlying payment mechanisms. A payment matrix that contains clearing payments in accordance with claims rules is a transfer scheme, which is not necessarily uniquely determined. This article is the first to provide the complete characterization of all such transfer schemes. Our characterization relies on additional cash vectors, which summarize the payments in excess of the minimum clearing payments. The set of such vectors is shown to be homeomorphic to the set of transfer schemes. We introduce a recursive procedure to compute any additional cash vector, and thereby indirectly a corresponding transfer scheme. The characterization opens up the opportunity for a network-based axiomatic analysis of transfer rules, which prescribe clearing payments for each financial network. In fact, we show that the characterization can be used to provide new axiomatizations of transfer rules in which each agent pays its creditors in accordance with the proportional claims rule

Decentralization and mutual liability rules

This paper builds on the recent work of Groote Schaarsberg et al. (Math Methods Oper Res 87(3):383–409, 2018) on mutual liability problems. In essence, a mutual liability problem comprises a financial network in which agents may have both monetary individual assets and mutual liabilities. Here, mutual liabilities reflect rightful monetary obligations from past bilateral transactions. To settle these liabilities by reallocating the individual assets, mutual liability rules are analyzed that are based on centralized bilateral transfer schemes which use a certain bankruptcy rule as its leading allocation mechanism. In this paper we derive a new characterization of mutual liability rules by taking a decentralized approach instead, which is based on a recursive individual settlement procedure. We show that for bankruptcy rules that satisfy composition, this decentralized procedure always leads to the same allocation as the one prescribed by the corresponding mutual liability rule based on centralized bilateral transfer schemes. Finally, we introduce a new reduction method for mutual liability problems and prove that any bankruptcy-rule-based mutual liability rule is invariant with respect to such a reduction

Duality in Financial Networks

This article introduces the concept of duality in financial networks. In bankruptcy problems, in which a bankrupt entity divides its non-negative assets among a group of claimants, duality of bankruptcy rules entails the division of losses versus gains. Financial networks generalize bankruptcy problems by allowing for multiple agents with individual assets interconnected by mutual claims. We show that allowing for negative assets is imperative to adequately formulate dual financial networks and dual bankruptcy problems. We show that there is a one-to-one correspondence between payment schemes based on bankruptcy rules in a financial network and payment schemes based on the dual of those bankruptcy rules in the dual financial network. Moreover, dual financial networks enable us to define dual transfer rules and dual allocation rules. We show that transfer rules based on self-dual bankruptcy rules need not necessarily be self-dual, whereas allocation rules based on self-dual bankruptcy rules are always self-dual

Dynamic Stability of Cooperative Investment under Uncertainty

This article models the inherent cooperative and non-cooperative incentives of stakeholders in investment projects in a novel way by combining concepts from co operative game theory and real options theory. As stakeholders have outside options, in the sense that they may terminate negotiations with the current coalition and join another, we introduce and analyze a coalitional and dynamic stability concept. We show that investment projects, in which cooperation between stakeholders is necessary, are more prone to coalitional instability when there are insufficient synergies between the stakeholders. We characterize the proportional investment scheme as the investment scheme that maximizes the total project value and that results in the earliest investment timing. A failure to implement proportional investing leads to the formation of a smaller, less efficient, coalition. The vulnerability to fail is exacerbated in a market that is characterized by high profit growth and low profit uncertainty, or vice versa. Finally, we explicitly consider one-leader investment projects and characterize the prioritized investment scheme that maximizes the value of the leader. We show that the same market conditions govern the stability of the prioritized investment scheme, which contributes to the robustness of our results

Duality in Financial Networks

This article introduces the concept of duality in financial networks. In bankruptcy problems, in which a bankrupt entity divides its non-negative assets among a group of claimants, duality of bankruptcy rules entails the division of losses versus gains. Financial networks generalize bankruptcy problems by allowing for multiple agents with individual assets interconnected by mutual claims. We show that allowing for negative assets is imperative to adequately formulate dual financial networks and dual bankruptcy problems. We show that there is a one-to-one correspondence between payment schemes based on bankruptcy rules in a financial network and payment schemes based on the dual of those bankruptcy rules in the dual financial network. Moreover, dual financial networks enable us to define dual transfer rules and dual allocation rules. We show that transfer rules based on self-dual bankruptcy rules need not necessarily be self-dual, whereas allocation rules based on self-dual bankruptcy rules are always self-dual

On the Compatibility of Composition Axioms in Financial Networks

This article introduces composition down and composition up in financial networks, and analyzes their compatibility. The starting point for the analysis is the outcome that is prescribed by a rule. For example, a transfer rule prescribes, for each financial network, a clearing payment matrix that contains mutual payments between the agents to settle their mutual liabilities. However, as it turns out, the assets of some of the agents in the financial network are either undervalued or overvalued, making the proposed outcome infeasible to carry out. In such cases, one has the option to either apply the rule to the new situation, or reapply the rule to an appropriately adjusted situation that honors the initial outcome. A composition axiom requires that both options are equivalent to all the agents. In the context of financial networks, there can exist various adequate versions of the two composition axioms. Interestingly, the adequate versions of the two composition axioms that are compatible for allocation rules are not compatible for transfer rules in the sense that no transfer rule can satisfy them simultaneously. Nevertheless, we show that there exist alternative adequate versions of the two composition axioms that are compatible with respect to transfer rules. In fact, we show that the transfer rules that either always prescribe the bottom payment matrix, or the top payment matrix, satisfy the two composition axioms simultaneously

Reduced-order modelling for prediction of aircraft flight dynamics: Based on indicial step response functions investigating agile aircraft undergoing rapid manoeuvres

During aircraft design,multiple tools are utilised to inspect the performance of the configuration. As the design matures, higher fidelity analyses are conducted to predict the flight dynamics of the aircraft. These analyses are conducted by using semi-empirical relations, numerically analysing flow behaviour, conducting wind-tunnel tests and performing scaled test flights. However, Semi-empirical relations might not hold for next generation aircraft and wind tunnel testing and scaled test flights are extensive and are also prone to accuracy issues. A best of both worlds can be found in numerical analysis. However, an increase in flow fidelity modelling comes with an increase in computational cost. Besides, complete analysis of all possible manoeuvres of a design increases the number of computations significantly. Current methods cope with this issue by using flight dynamics models based on so called stability derivatives, instantaneous values which couple flight state parameters to aerodynamic loads to predict aircraft flight dynamics. However, these models do not take into account time dependency. Therefore, these methods do not accurately predict the flight dynamics of agile aircraft, such as unmanned combat aerial vehicles, undergoing rapid manoeuvres where unsteadiness dominates flow behaviour. This conventional reduced-order modelling method, in which samples of the full-order model are taken in the form of stability derivatives, causes design iterations to be analysed inaccurately. The objective of this report is to investigate reduced-order modelling for flight dynamics prediction, thereby comparing conventional techniques to a method which does take into account unsteadiness in flow behaviour.The method investigated is based on indicial step response functions, which are samples in the form of unsteady aerodynamic flow behaviour functions of the full-order model. The idea is that once these samples are known, any flight manoeuvre can be analysed within minutes. Research found in literature has assessed some of the capabilities and limitations of this method, but not yet applied this to flight dynamics prediction. The research described within this report will address this gap by using two test cases. The first testcase is used to assess the assumptions made in literature, on aerodynamics loads modelling, by applying the method on a two-dimensional airfoil in subsonic flow conditions. It was found that the indicial step response functions are indeed representing the full-order model, thereby taking into account unsteady flow behaviour in aerodynamic loads prediction. In longitudinal motions, the angle of attack and pitch rate effect need to be taken into account to predict lift, drag and pitching moments. Multiple frequencies of the same manoeuvre can be analysed within minutes once the samples are calculated. Results show that the accuracy of the predictions becomes a trade-off issue between samples calculated and accuracy required. The second testcase is used to apply the indicial response functions to flight dynamics prediction of an agileunmanned bomber aircraft undergoing fast manoeuvres. A longitudinal-directional climbing manoeuvre was calculated by developing a flight dynamics model based on stability derivatives. The flow behaviour encountered during this manoeuvre was analysed to include highly unsteady and non-linear phenomena (e.g. vortices and flow separation) at higher angles of attack. By comparing the results of themethod under investigation to the full-order solutions, it was shown that aerodynamic flight dynamics predictions were accurate in capturing unsteady behaviour and weak non-linear flow behaviour. However, the samples proved to be inaccurate in representing behaviour in highly non-linear regions. Concluding, this means that indicial step response functions provide more accurate flight dynamics predictions than conventional stability derivatives in representing unsteady flow behaviour. The accuracy of the predictions are highly dependent on the samples chosen. Several samples suffice to predict the unsteady behaviour for linear and weak non-linear flow regions of the flightmanoeuvre. If surrogate modelling is applied, the method can become more computational efficient than conducting multiple full-order time-marching numerical calculations. It is recommended that more research is performed on indicial step response functionsin capturing highly non-linear flow behaviour, as the research showed that the size of the samples affects the flow behaviour representation.Aerospace Engineering | Flight Performance and Propulsio