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Since you own 50% of the shares in the corporation, you can file a petition in court to stop the buyout by showing that you and your partner are hopelessly deadlocked on an agreement, or he is conducting fraudulent or oppressive actions toward you.
However, in NYS it is up to the court’s to decide under the NYS Business Corporations Law what the proper remedy is for the dispute. In that context, a judge may conclude that a buy-out may be a proper remedy for your situation.
The BCL law gives your partner the option to buy you out for the fair value of your ownership share when there is not written shareholder’s agreement. But they must make that election within 90 days after you have filed your papers. However, you will have a right to have an accounting of all of the books and records in discovery, and your accountant (expert) will examine the financials and records and determine a value of the corporation. This process is not short, is time consuming and can be expensive.
So yes, you can file an action in court, and then during the discovery phase you can obtain financial, books, records, etc. and make determination on the value.
I hope this helps.