Pricing Algorithm Research Articles

Reverse mortgages through artificial intelligence: new opportunities for the actuaries

In its basic structure, the reverse mortgage (RM) is a contract where a home owner borrows a part or the totality of the future liquidation value of his home at the time of his death. The risks that are borne by the lender are linked to the volatility of the real estate market, that is the house price risk, the financial market risk, that is the interest rate risk, and the uncertainty of the borrower’s lifetime, that is the longevity risk. The quantification of the future liquidation value and its valuation at the issue time is fundamental in the construction of the RM contract either in the perspective of the lender or in the one of the borrower. In the paper, we explore the use of neural networks to project the real estate market data; this approach allows to obtain a predictive analysis of the pricing process and indeed provides a dynamic pricing algorithm.

A pricing problem with unknown arrival rate and price sensitivity

We study a pricing problem with finite inventory and semi-parametric demand uncertainty. Demand is a price-dependent Poisson process whose mean is the product of buyers’ arrival rate, which is a constant lambda , and buyers’ purchase probability q(p), where p is the price. The seller observes arrivals and sales, and knows neither lambda nor q. Based on a non-parametric maximum-likelihood estimator of (lambda ,q), we construct an estimator of mean demand and show that as the system size and number of prices grow, it is asymptotically more efficient than the maximum likelihood estimator based only on sale data. Based on this estimator, we develop a pricing algorithm paralleling (Besbes and Zeevi in Oper Res 57:1407–1420, 2009) and study its performance in an asymptotic regime similar to theirs: the initial inventory and the arrival rate grow proportionally to a scale parameter n. If q and its inverse function are Lipschitz continuous, then the worst-case regret is shown to be O((log n / n)^{1/4}). A second model considered is the one in Besbes and Zeevi (2009, Section 4.2), where no arrivals are involved; we modify their algorithm and improve the worst-case regret to O((log n / n)^{1/4}). In each setting, the regret order is the best known, and is obtained by refining their proof methods. We also prove an Omega (n^{-1/2}) lower bound on the regret. Numerical comparisons to state-of-the-art alternatives indicate the effectiveness of our arrivals-based approach.

Fast core pricing algorithms for path auction

Path auction is held in a graph, where each edge stands for a commodity and the weight of this edge represents the prime cost. Bidders own some edges and make bids for their edges. The auctioneer needs to purchase a sequence of edges to form a path between two specific vertices. Path auction can be considered as a kind of combinatorial reverse auctions. Core-selecting mechanism is a prevalent mechanism for combinatorial auction. However, pricing in core-selecting combinatorial auction is computationally expensive, one important reason is the exponential core constraints. The same is true of path auction. To solve this computation problem, we simplify the constraint set and get the optimal set with only polynomial constraints in this paper. Based on our constraint set, we put forward two fast core pricing algorithms for the computation of bidder-Pareto-optimal core outcome. Among all the algorithms, our new algorithms have remarkable runtime performance. Finally, we validate our algorithms on real-world datasets and obtain excellent results.

Platform Design When Sellers Use Pricing Algorithms

Using both economic theory and Artificial Intelligence (AI) pricing algorithms, we investigate the ability of a platform to design its marketplace to promote competition, improve consumer surplus, and even raise its own profits. We allow sellers to use Q-learning algorithms (a common reinforcement-learning technique from the computer-science literature) to devise pricing strategies in a setting with repeated interactions, and consider the effect of platform rules that reward firms that cut prices with additional exposure to consumers. Overall, the evidence from our experiments suggests that platform design decisions can meaningfully benefit consumers even when algorithmic collusion might otherwise emerge but that achieving these gains may require more than the simplest steering policies when algorithms value the future highly. We also find that policies that raise consumer surplus can raise the profits of the platform, depending on the platform's revenue model. Finally, we document several learning challenges faced by the algorithms.

FORECASTING PRICES IN THE RENTAL HOUSING MARKET WITH MACHINE LEARNING METHODS

The study of pricing factors in the market of the short-term rental has been done. Airbnb was chosen as the object of the study; it is a platform for accommodation, search, and rental around the world. At the beginning of 2021, the company offers 7 million homes from more than 220 countries. The Data Science methods play a significant role in the company's success. One of the key algorithms of the company is the pricing algorithm. Using the "Price Recommendations" feature, the homeowner can analyze which dates are most likely to be booked at the current price and which are not, it helps form a favorable offer. The system calculates the recommended cost of housing based on hundreds of parameters, some of which are easy to recognize, but there are less obvious factors that can also affect demand. The paper proposes an algorithm for identifying implicit pricing factors in the short-term rental market using machine learning methods, which includes: 1) data mining and data preparation; 2) building and analysis of linear regression models; 3) building and analysis of nonlinear regression models. The study was based on ads from the Airbnb site in Washington and New York using scripts developed in Python. The following models are built and analyzed: simple linear regression, multiple linear regression, polynomial regression, decision trees, random forest, and boosting. The results of the study showed that the most important factors are accommodates, cleaning_fee, room_type, bedrooms. But based on the model evaluation criteria, they cannot be used for implementation: linear models are of low quality, while the random forest, boosting, and trees are overfitted. Still the results can be used in conducting business analysis.

Differential Machine Learning

Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing and risk approximations, online, in real-time, with convergence guarantees. Our machinery is applicable to arbitrary Derivatives instruments or trading books, under arbitrary stochastic models of the underlying market variables. It effectively resolves computational bottlenecks of Derivatives risk reports and capital calculations. Differential ML is a general extension of supervised learning, where ML models are trained on examples of not only inputs and labels but also differentials of labels wrt inputs. It is also applicable in many situations outside finance, where high-quality first-order derivatives wrt training inputs are available. Applications in Physics, for example, may leverage differentials known from first principles to learn function approximations more effectively. In finance, AAD computes pathwise differentials with remarkable efficacy so differential ML algorithms provide extremely effective pricing and risk approximations. We can produce fast analytics in models too complex for closed-form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or regulations like XVA, CCR, FRTB or SIMM-MVA. TensorFlow implementation is available on https://github.com/differential-machine-learning

Performance comparison of two market algorithms for providing support services todistribution systems

Several market algorithms, such as Fast Locational Marginal Pricing (FLMP) and Receding Horizon Control (RHC), have shown the ability to cope with grid congestion. The RHC algorithm can cope with fluctuations in power consumption and generation but is computationally intensive due to the larger search space within the time horizon. The FLMP algorithm is not complex but does not utilize a horizon with information on future consumption and generation. This paper demonstrates a performance comparison between the FLMP and Horizon Marginal Pricing (HMP) algorithm. HMP is an algorithm that combines the simplicity of the FLMP algorithm with the time horizon possibilities of the RHC algorithm. The HMP algorithm uses the predicted generation profile to adjust the bid curves, such that consumption shifts to moments with more renewable generation available. Simulations are carried out to compare the performance between the HMP and FLMP algorithms. The results show comparable performance between the FLMP and HMP, whilst the FLMP computes the simulation faster and requires less bandwidth.

Third Party Pricing Algorithms and the Intensity of Competition

Third Party Pricing Algorithms and the Intensity of Competition

Pricing algorithms as a tool of doing business: the antitrust risks and compatibility issues

The subject of the study is the concept of “price algorithm”, the problems associated with risks of qualification of pricing algorithms use as a violation of the competition law. Based on the analysis of Russian and case law enforcement practice, it is concluded that under certain conditions, the use of pricing algorithms can be recognized as compatible with the requirements of the competition law. However, undertakings should carefully consider using pricing algorithms to avoid restriction of competition.

Mobile Cloud Storage Over 5G: A Mechanism Design Approach

In order to meet the increasing demand for the data storage, 5G wireless networks embodying mobile edge computing (MEC) features arise as a compelling solution. In this paper, the dense heterogeneous network (HetNet) and the MEC infrastructure are exploited to propose a mobile cloud storage framework that minimizes the data transmission delay. The proposed framework is composed of two parts: A data management with error correction (DMEC) scheme, and a radio resource management (RRM) scheme. The DMEC scheme, derived from the redundant array of inexpensive disks (RAID) technology, is implemented in the user equipment (UE) side, and it intelligently exploits the overlapping coverage of HetNet to minimize the transmission delay. On the other hand, the RRM scheme, based on mechanism design, presents the physical resource block allocation problem as a graph coloring problem and performs the radio resource allocation in multiuser scenario to maximize the network performance. The RRM scheme also comprises a pricing algorithm, which calculates the price a UE needs to pay for the resources. The proposed RRM scheme exhibits several desirable characteristics such as incentive compatibility, efficiency, and truthfulness, all derived from the Vickrey–Clarke–Groves mechanism. Simulation results are presented, showing that the proposed framework when compared to baseline techniques, minimizes the transmission delay by $10^2$ %, which places our proposal as effective and efficient solution for the mobile cloud storage problem.

Competition in Pricing Algorithms

We document new facts about pricing technology using high-frequency data, and we examine the implications for competition. Some online retailers employ technology that allows for more frequent price changes and automated responses to price changes by rivals. Motivated by these facts, we consider a model in which firms can differ in pricing frequency and choose pricing algorithms that are a function of rivals' prices. In competitive (Markov perfect) equilibrium, the introduction of simple pricing algorithms can generate price dispersion, increase price levels, and exacerbate the price effects of mergers.

Benchmarking machine-learning software and hardware for quantitative economics

We investigate the performance of machine-learning software and hardware for quantitative economics. We show that the use of machine-learning software and hardware can significantly reduce computational time in compute-intensive tasks. Using a sovereign default model and the Least Squares Monte Carlo option pricing algorithm as benchmarks, we show that specialized hardware and software speed up calculations by up to four orders of magnitude when compared to programs written in popular high-level programming languages, such as MATLAB, Julia, Python/Numpy, and R, and high-performing low-level languages such as C++.

Dynamic pricing and matching in ride‐hailing platforms

AbstractRide‐hailing platforms such as Uber, Lyft, and DiDi have achieved explosive growth and reshaped urban transportation. The theory and technologies behind these platforms have become one of the most active research topics in the fields of economics, operations research, computer science, and transportation engineering. In particular, advanced matching and dynamic pricing (DP) algorithms—the two key levers in ride‐hailing—have received tremendous attention from the research community and are continuously being designed and implemented at industrial scales by ride‐hailing platforms. We provide a review of matching and DP techniques in ride‐hailing, and show that they are critical for providing an experience with low waiting time for both riders and drivers. Then we link the two levers together by studying a pool‐matching mechanism called dynamic waiting (DW) that varies rider waiting and walking before dispatch, which is inspired by a recent carpooling product Express Pool from Uber. We show using data from Uber that by jointly optimizing DP and DW, price variability can be mitigated, while increasing capacity utilization, trip throughput, and welfare. We also highlight several key practical challenges and directions of future research from a practitioner's perspective.

Branch-and-cut-and-price for the cardinality-constrained multi-cycle problem in kidney exchange

The establishment of kidney exchange programs has dramatically improved rates for kidney transplants by matching donors to compatible patients who would otherwise fail to receive a kidney for transplant. Rather than simply swapping kidneys between two patient-donor pairs, having multiple patient-donor pairs simultaneously donate kidneys in a cyclic manner enables more patients to receive a kidney for transplant. For practicality reasons, the cycles must be limited to short lengths. Finding these cycles can be accomplished by solving the Cardinality-constrained Multi-cycle Problem, which generalizes the Prize-collecting Assignment Problem with constraints that bound the length of the subtours. This paper presents a series of additions to existing works—new constraints, some polyhedral results, new separation algorithms and a new pricing algorithm—and integrates them in the first branch-and-cut-and-price model of the problem. The model is shown to empirically outperform the state-of-the-art by solving 149 of 160 standard benchmarks, compared to 115 by the position-indexed chain-edge formulation and 114 by the position-indexed edge formulation.

A lexicographic pricer for the fractional bin packing problem

We propose an exact lexicographic dynamic programming pricing algorithm for solving the Fractional Bin Packing Problem with column generation. The new algorithm is designed for generating maximal columns of minimum reduced cost which maximize, lexicographically, one of the measures of maximality we investigate. Extensive computational experiments reveal that a column generation algorithm based on this pricing technique can achieve a substantial reduction in the number of columns and the computing time, also when combined with a classical smoothing technique from the literature.

A branch and price algorithm to solve the Quickest Multicommodity k-splittable Flow Problem

In the literature on Network Optimization, k-splittable flows were introduced to enhance modeling accuracy in cases where an upper bound on the number of supporting paths for each commodity needs to be imposed, thus extending the suitability of network flow tools for an increased number of practical applications. Such modeling feature has recently been extended to dynamic flows with the introduction of the novel strongly NP-hard Quickest Multicommodity k-splittable Flow Problem (QMCkFP). Such a flows over time problem asks for routing and scheduling of each commodity demand through at most k different paths in a dynamic network with arc capacities per time step, while minimizing the time required by the overall process. In this work, we propose the first exact algorithm for solving the QMCkSFP. The developed technique falls within the Branch and Price class and is based on original relaxation, pricing and branching procedures. Linearization and variable substitution are used to obtain the relaxation problem from the path-based formulation of the QMCkSFP. The pricing problem is modeled as a Shortest Path Problem with Forbidden Paths with additional node-set resources on a time expansion of the original digraph and is solved via a tailored dynamic programming algorithm. Two branching rules are designed for restoring feasibility whenever k-splittable or binary variable domain constraints are violated. The results of an extensive batch of computational experiments conducted on small to medium-size reference instances are presented, showing a highly satisfactory performance of the proposed algorithm. The paper concludes with a discussion on further lines of research.

Dynamic Pricing with External Information and Inventory Constraint

A merchant dynamically sets price in each time period when selling a product over a finite time horizon, with a given initial inventory. The merchant utilizes new external information that is observed at the beginning of each time period, while the demand function - how the external information and the price jointly impact that single-period demand distribution - is unknown. The merchant's decision, setting price dynamically, serves dual roles to learn the unknown demand function and to balance inventory, with an ultimate objective to maximize the expected cumulative revenue. We characterize and prove a full spectrum of relations between the order of optimal expected cumulative revenue achieved in three decision-making regimes: the merchant's online decision-making regime, a clairvoyant regime with complete knowledge about the demand function and, and a deterministic regime where all the uncertainties are relaxed to the expectations. In the analyses, we derive an unconstrained representation of the optimality gap for generic constrained online learning problems, which renders tractable lower and upper bounds for the expected revenue achieved by dynamic pricing algorithms between different regimes. This analytical framework also inspires the design of two dual-based history-dependent dynamic pricing algorithms for the clairvoyant regime and the online regime.

A Convex Optimization Algorithm for Electricity Pricing of Charging Stations

The problem of electricity pricing for charging stations is a multi-objective mixed integer nonlinear programming. Existing algorithms have low efficiency in solving this problem. In this paper, a convex optimization algorithm is proposed to get the optimal solution quickly. Firstly, the model is transformed into a convex optimization problem by second-order conic relaxation and Karush–Kuhn–Tucker optimality conditions. Secondly, a polyhedral approximation method is applied to construct a mixed integer linear programming, which can be solved quickly by branch and bound method. Finally, the model is solved many times to obtain the Pareto front according to the scalarization basic theorem. Based on an IEEE 33-bus distribution network model, simulation results show that the proposed algorithm can obtain an exact global optimal solution quickly compared with the heuristic method.

Two-Stage IoT Device Scheduling With Dynamic Programming for Energy Internet Systems

With the rapid evolution of electric systems, there has been a significant demand for energy Internet (EI) systems that allow sustainable and environmentally friendly energy management. Several research efforts regarding EI systems have been aimed at providing reliable, efficient, and cost-effective techniques. In this paper, we propose a novel algorithm and system for real-time electricity pricing and scheduling. Our algorithm consists of a two-stage operation. The first stage performs real-time pricing to determine the maximum electricity consumption while the second stage performs Internet of Things (IoT) device scheduling. In the second stage, the optimization framework for scheduling is modeled as a 0–1 Knapsack problem; therefore, the solutions to the optimization problem are computed using a dynamic programming framework. Through intensive simulations with well-defined parameters, it is verified that the proposed scheme provides several features, especially reductions in electricity bills with the appropriate parameter settings.

자가학습 가격 책정 알고리즘과 암묵적 담합에 관한 시뮬레이션 분석

자가학습 가격 책정 알고리즘과 암묵적 담합에 관한 시뮬레이션 분석