1. Arbitrage is a referendum on a transactional view of relationships. Robert Miller can only relate to people if he can buy them. His wife only stays with him because of the lifestyle it affords her. He can only relate to his children through his business- he reminds his daughter "you work for me," and his son, who has no business acumen, is referred to as an idiot and given minimal screen time. His daughter wonders what they would even talk about if they spent time together outside the office. His mistress is with him because he funds her art and provides her with a place to live. In each case, he gets what he wants by spending the massive amounts of money he has earned through his hedge fund, rather than through sincere interest or care for another human being. People are assets to be manipulated for gain. I know people, far less successful than Miller, that view the world this way and I could see their personalities reflected in Miller's relationship.
What makes this movie cynical, and I think accurate, is that (*SPOILER ALERT*) Miller wins. Though it is at the cost of the relationships with his wife and daughter, the life of his mistress, and any integrity he might have once had; these things are secondary to the successful sale of his company and avoiding any direct personal harm.
2. Because Miller is purely objective-oriented at the expense of all else, he rarely exhibits sincere concern for another human being or regret. In fact he is often called out on it by the people closest to him. When he enters his birthday party at the beginning of the film he is handed gifts to give to his grandkids by his servants, missing the point that what matters is remembering the person and putting thought into their gifts, not the act of spending money. After giving a speech to his family about how they are "what's really important" his daughter observes that last time he gave a speech like that the company lost a huge deal and questions him about what is really going on. Whenever Miller says the word "sorry" it is always with the intent of getting something from the person he is talking to and often is followed by the promise of money or gifts to allay the anger being thrown at him.
He also uses the damage his actions would inflict on others as a way of avoiding responsibility for them. Whenever he is attacked for his illegal business practices he hides behind the damage that would be done to his shareholders, "real people would be hurt!!" Whenever he is taken to task for the way he is neglecting or mistreating his family for the sake of his business he claims that "everything I do is for this family!!" It is clear from the way that he sacrifices that his relationship with them that this is not a sincere sentiment. Concern and regret are nothing more than bargaining tactic to him.
3. That being said there are moments of sincerity for Miller. After the car crash that kills his mistress, Miller expresses sincere anger and frustration. None of this is in concern over the dead woman in his car, but rather over how this affects him and the pending sale of his business. In fact, he never expresses sincere regret over her death beyond how it affects his bottom line.
The only time he is truly happy in this movie is after negotiating the sale of his company at a table with a contract written on the back of a menu. After all the frustrations with the audit not being cleared, his car crash creating legal trouble, and his family falling apart; he has won what really matters to him- $525MM. He even tries to win the conversation afterwards: "What would you have paid?"
"$600. What would you have taken?"
"$475"
"Then we made a good deal"
"Yeah.... actually I would have taken $400"
4. Though Miller cynically treats his personal relationships as transactions where he can maximize his return for minimal effort, he is successful because everyone around him has a similar worldview. He is just far better at the "game" than they are. The policeman spearheading the investigation of the car crash was willing to falsify evidence and send an innocent man to jail in order to nail a "rich bastard to the wall." Miller wins because he is smarter, used to being lied to, and has the resources to expose the falsehood. Miller's wife tries to manipulate their daughter when she is most vulnerable in order to strip Miller of everything he has and reassert agency in her own life. She is outmaneuvered by Miller and ultimately her will is broken. Mayfield is just as skilled as Miller in manipulating events to drive down the price of Miller's company before making an offer. Once Miller convinces Mayfield that their objectives align, Mayfield is more than willing to overlook a $400MM hole in the books for the "greater good" of his stock price.
Miller's daughter, Brooke, is presented as a contrast to this philsophy. She realizes the books are being cooked and confronts her father about the $400MM hole in their accounting. Miller asserts his power over his daughter as an employer and a father and frames her exposing the lie as a choice between her integrity/career and her family. Their contrast in worldviews is displayed in the contrasted between his dark suit and her light dress. As she mulls over this information she is shown wearing black. Ultimately she succumbs to his worldview, accepting it even if she does not believe it, and we see her in a white dress that no longer means anything.
5. Jimmy is an important counterpoint to Miller in the film, because he is the one character that is defined by his integrity and cannot be bought. Jimmy's father had been Miller's driver. Miller calls on Jimmy for help after the car crash after years of being out of contact because, as the detective points out later in the movie, Jimmy is expendable to Miller. Jimmy repeatedly turns down offers of money as he sees doing the right thing as it's own end and will not take payment for it or take money to compromise his integrity.
The screen-writer manipulates the audience into rooting for Miller when his interests align with Jimmy's. When Miller is trying to prove Jimmy's innocence the audience wants him to get Jimmy off the hook for obstruction of justice because Jimmy is a shining beacon of morality. The sinking realization after he succeeds is that this was not done for Jimmy's benefit, but for Miller's. The good guy benefited, but the bad guy won.
At the end of the film Miller offers Jimmy money in order to assuage his guilt for nearly ruining his life. Jimmy is the one character who is able to take money from Miller without compromising his integrity, in fact he swears to do something good with it (open an Applebee's). Because of this Jimmy is the one character able to end this movie with a positive ledger, both financially and morally.
Arbytrage
Audit report says: See this film immediately.
