Dynamic Bid Research Articles

Market consistent bid-ask option pricing under Dempster-Shafer uncertainty

We refer to the discrete-time market model under ambiguity introduced in [Cinfrignini, A., Petturiti, D. and Vantaggi, B., Dynamic bid–ask pricing under Dempster-Shafer uncertainty. J. Math. Econ., 2023a, 107, 102871], formed by a frictionless risk-free bond and a non-dividend paying stock with bid-ask spread. For a European derivative, we generalize the classical binomial pricing formula by allowing for bid-ask prices and investigate the properties of the ensuing replicating strategies. Next, for an American derivative, we propose a backward bid-ask pricing procedure and prove that the resulting discounted price processes are the bid-ask Choquet-Snell envelopes of the discounted payoff process, respectively. Moreover, for an American call option, we prove a generalization of the well-known Merton's theorem [Merton, R.C., Theory of rational option pricing. Bell J. Econ. Manage. Sci., 1973, 4, 141–183] holding for both the bid and the ask price processes. Finally, we introduce a market consistent calibration procedure and show the use of the calibrated model in bid-ask option pricing.

Energy scheduling optimisation of an islanded microgrid via artificial bee colony guided by global best, personal best and asynchronous scaling factors

ABSTRACTAn islanded microgrid (IMG) having renewable energy sources (RES), dispatchable sources and battery energy storage (BES) is an effective approach to supply the electricity in remote areas. The reliable operation of IMG is quite complex and challenging task, due to uncertain behaviour of RES, loads and energy bid. In this paper, an IMG is simulated to maximise the revenue considering a dynamic optimisation objective subjected to various constraints of system components for two different cases, i.e. considering the stationary and the dynamic energy bid. Artificial bee colony (ABC) and its variants based on global best (GABC), and global and personal best with asynchronous scaling factors (GPSABC) are implemented and the obtained results are also compared with the existing optimisation techniques. Results of GPSABC improve the revenues and offers better accuracy and stability parameters. Further, the effect on revenue results with different ramp rates of diesel generators is described through GPSABC.

Revenue management for make-to-order manufacturing systems with a real-life application

Due to successful applications of revenue management in the airline industry, in recent years, there has been a growing interest to adopt revenue management in make-to-order (MTO) manufacturing systems. Several interrelated decision problems such as order acceptance/rejection, short-term capacity planning, due date assignment, and order scheduling need to be studied simultaneously in order to manage revenues effectively in MTO manufacturing systems. Both the producer’s and customer’s requirements need to be taken into account through some negotiation mechanisms that are sensitive to the service-level reputation of the manufacturing companies. In this article, we propose a new dynamic bid price–based revenue management model that considers all of the aforementioned decision problems simultaneously. A simulation optimization approach is utilized in order to determine the best possible values of control parameters for bid price, due date assignment, and price increment/reduction mechanisms. The performance of the proposed integrated revenue management model is tested on both a hypothetical example and a real problem of a bridal gown company. The computational results show that the proposed model provides significant improvements in total revenue compared to other static and dynamic bid price policies.

A dynamic bid price approach for the seat inventory control problem in railway networks with consideration of passenger transfer

Railway seat inventory control aims to maximize ticket sale profits by determining a selling policy on the reservation horizon. This paper introduces a dynamic bid price approach in railway seat inventory control problem. Multi-dimensional demand is taken into consideration in modeling the problem, in which passenger transfer is our main focus. A new approximate approach is designed to this problem. Numerical examples are presented to evaluate the efficiency of this approach. Simulation experiments are conducted to verify the impact of transfer under different scenarios.

Dynamic Bid Pricing for an Optimized Resource Utilization in Small and Medium Sized Enterprises

Sales revenues of small and medium-sized enterprises are subject to seasonal fluctuation. This leads often to overloaded or underutilized manufacturing resources. Either way, this results in revenue losses. Therefore, companies have to optimize their resource utilization. This paper describes a new methodology for a dynamic bid price system by using correlations of revenue management in production planning to level the resource utilization. The methodology supports especially small and medium-sized enterprises, which are often affected by additional work shifts across seasons. Furthermore, the proposed method points out dependencies between costs and capacity to avoid financial losses. The method has been developed and is being tested in collaboration with two small and medium-sized enterprises.

Dynamic Concave Performance Measures and Bid and Ask Prices with Stochastic Liquidity

In this article we provide a new definition of concave conditional performance measures. We prove a duality to conditional risk measures. New dynamic performance measures based on dynamic risk measures are established. We are able to derive dynamic bid and ask prices with respect to a stochastic liquidity process by modelling the market as a passive counterparty which accepts at zero cost a certain collection of cash flows. An economical abnormality is detected in a comparable definition of bid and ask prices existing in literature. Using the binomial model, analytic formulas of bid and ask prices of European options are given.

Scalable Dynamic Bid Prices for Network Revenue Management in Continuous Time

This study develops an approximate optimal control problem to produce time‐dependent bid prices for the airline network revenue management problem. The main contributions of our study are the analysis of time‐dependent bid prices in continuous time and the use of splines to modify the problem into an approximate second‐order cone program (ASOCP). The spline representation of bid prices permits the number of variables to depend solely on the number of resources and not on the size of the booking horizon. The advantage of this framework is the ASOCP's scalability, which we demonstrate by solving for bid prices on an industrial‐sized network. The numerical experiments highlight the ASOCP's ability to solve industrial sized problems in seconds.

Dynamic Multi-Factor Bid–Offer Adjustment Model:A Feedback Mechanism for Dealers(Market Makers) to Deal (Grapple) with theUncertainty Principle of the Social Sciences

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DYNAMIC CONIC FINANCE: PRICING AND HEDGING IN MARKET MODELS WITH TRANSACTION COSTS VIA DYNAMIC COHERENT ACCEPTABILITY INDICES

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.

On optimal bidding in sequential procurement auctions

We investigate the problem of optimal bidding for a firm that in each period procures items to meet a random demand by participating in a finite sequence of auctions. We develop a new model for a firm where its item valuation derives from the sale of the acquired items via their demand distribution, sale price, acquisition cost, salvage value and lost sales. We establish monotonicity properties for the value function and the optimal dynamic bid strategy and we present computations.

Computing Time-Dependent Bid Prices in Network Revenue Management Problems

We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it naturally provides dynamic bid prices that depend on how much time is left until departure. We show that our method provides an upper bound on the optimal total expected revenue and that this upper bound is tighter than the one provided by the widely known deterministic linear programming approach. Furthermore, it is possible to use the bid prices computed by our method as a starting point in a dynamic programming decomposition-like idea to decompose the network revenue management problem by the flight legs and to obtain dynamic and capacity-dependent bid prices. Our computational experiments indicate that the proposed method improves on many standard benchmarks.

Dynamic bidding analysis in power market based on the supply function

This paper presents a dynamic bidding model of the power market based on the Nash equilibrium and a supply function. The new model is composed of different dynamic systems and semismooth equations by means of the nonlinear complementarity method. Comparing with those existing bidding models, the remarkable characteristic of the new model is twofold: First, it adopts a dynamic bid so that the bidding limit point is the Nash equilibrium point of the market; Second, it considers the system requirement and the market property such as involving the transmission constraints in the network, and using a supply function which is suitable for the oligopolistic competitive power market. All of these imply that the new model is very close to the practical power market. The computation of the dynamic model is discussed by using the semismooth theory. A numerical simulation is presented to test the model behaviors in the uncogestion and the congestion cases, respectively. The numerical tests include the computing behavior of the dynamic model to reach Nash equilibrium points, the influence of the adjusted parameters and the system parameters to the Nash equilibrium, the local stability of the model, and the comparison of simulation effect between the proposed model and the Cournot model. The simulations show that the new bidding model is valid.

Dynamic Bid Prices in Revenue Management

We formally derive the standard deterministic linear program (LP) for bid-price control by making an affine functional approximation to the optimal dynamic programming value function. This affine functional approximation gives rise to a new LP that yields tighter bounds than the standard LP. Whereas the standard LP computes static bid prices, our LP computes a time trajectory of bid prices. We show that there exist dynamic bid prices, optimal for the LP, that are individually monotone with respect to time. We provide a column generation procedure for solving the LP within a desired optimality tolerance, and present numerical results on computational and economic performance.

Bid rotation and collusion in repeated auctions

This paper studies bidder collusion with communication in repeated auctions when no side transfer is possible. It presents a simple dynamic bid rotation scheme which coordinates bids based on communication history and enables intertemporal transfer of bidders’ payoffs. The paper derives a sufficient condition for such a dynamic scheme to be an equilibrium and characterizes the equilibrium payoffs in a general environment with affiliated signals and private or interdependent values. With IPV, it is shown that this dynamic scheme yields a strictly higher payoff to the bidders than any static collusion scheme which coordinates bids based only on the current reported signals.