The Absence of Arbitrage on the Complete Black-Scholes-Merton Regime-Switching Lévy Market

The main aim of the paper was to prove that the complete Black-Scholes-Merton regime-switching Lévy market is characterized by an absence of arbitrage. In the considered model, the prices of financial assets are described by the Lévy process in which the coefficients depend on the states of the Markov chain. Such a market is incomplete; in order to complete this market, jump financial instruments and power-jump assets were added. Then, an equivalent martingale measure was indicated and the conditions were determined so that the above model is characterized by the absence of arbitrage. Arbitrage is a trade that profits by exploiting the price differences of identical or similar financial instruments in different markets or in different forms. Thus arbitrage can be understood as risk-free profit for the trader.